First things first -- commingling service and non-service conductors in an auxiliary gutter is unwise, despite being Code-legal, so you were right to correct that situation.
Second, the grounding electrode conductor (and water system bonding termination) connecting into the meter pan grounding busbar is almost OK even though no separate EGC is routed from the meter pan to the service disconnects, as it falls under 250.64(D)(3):
(3) Common Location. A grounding electrode conductor
shall be connected in a wireway or other accessible enclosure on the supply side of the disconnecting means to·one
or more of the following, as applicable:
(1) Grounded service conductor(s)
(2) Equipment grounding conductor installed with the
feeder
(3) Supply-side bonding jumper
The connection shall be made with exothermic welding or
a connector listed as grounding and bonding equipment. The
grounding electrode conductor shall be sized in accordance
with 250.66 based on the service-entrance or feeder conductor(s) at the common location where the connection is made.
My prime concern here would be that that ground busbar may not be accessible due to the utility seals on the meter pan -- if that part of the meter pan is customer accessible though, then that's not an issue.
Third, the gutter bonding arrangement follows 250.80 and 250.92, so that's hunky-dory, except for the fact that the 6AWG copper wire used is one size too small -- 4AWG is the correct size system bonding jumper as per table 250.102(C)(1).
Finally, the bond conductor between the gutter bonding point and the service disconnecting means is...redundant. 250.92(B)(1) calls for service equipment enclosures to be bonded to the grounded conductor using a Code-compliant means, and the green screw in your service disconnect enclosure's neutral bar certainly qualifies!
So, you can remove the redundant (and undersized) bonding jumpers in the auxiliary gutter, as well as the existing gutter bonding jumper, and use a length of 4AWG bare copper to bond the gutter to an accessible point on the grounded conductor (such as the existing meter pan grounding busbar) as per option 1 in your drawings. If the existing meter pan grounding busbar is indeed inaccessible, then the grounding electrode (GEC) and water system bonding conductors will need to be replaced with longer ones that can be run into the auxiliary gutter, as that's where a grounding tap for this stuff will need to be installed, connecting the service neutral to the GEC, water system bond, and gutter.
Your Option 2, however, probably won't fly -- the use of a separate bonding conductor alongside the service conductors might get dinged by the AHJ as a 250.92(B) violation, and is a waste of copper anyhow! (In fact, a cleaner solution than Option 2 would be to remove the dang PVC nipples and replace them with rigid metallic ones fitted using listed bonding-type locknuts.)
As to your updated plan, that appears mostly correct -- 4AWG is big enough for the job as per table 250.66, while the bond of the grounded neutral conductor to the meter pan is in accordance with 250.80 and 250.92. However, I would route the grounding wires for the CATV and telephone systems directly to the gutter grounding and bonding busbar, using it as your intersystem bonding termination as well. This treats the auxiliary gutter as "an enclosure for service equipment" for the sake of 250.94 and eliminates the need to make irreversible compression-type or exothermically welded taps on the new grounding electrode conductor. Finally, I would remove the existing grounding electrode conductor and water system bonding conductor to avoid inadvertently paralleling the neutral and possibly causing stray currents in the water piping or grounding electrode systems.
Your real problem is a lost neutral.
That's why your voltages were going all 80-240V. The neutral wire broke between the panel and the pole. This needs to be fixed. Unless it's in your panel, it's the power company's problem and should be reported as a power outage, which it actually is. Shut off everything until it is.
If hooking up a ground significantly improves conditions, that diagnostically proves the neutral problem, but This is NOT a legitimate or safe fix!!! It should not be continued for even one more minute. Shut Everything Off and get that neutral fixed.
Since your panel does not appear to have a main breaker, you would need to call your power company and have them come out and pull the meter. They need to do that anyway to investigate the lost neutral.
Now might be a good time to get a meter pan which contains a main breaker. I would obtain it and have it ready for when the power company comes out to fix the neutral. They may just fit it for free, since they're in there anyway, and replacing beats troubleshooting.
Other stuff
The nice thing about a main breaker on the meter pan is if you turn it off, your entire panel is deenergized, which makes the panel safer to work in, and makes a whole-panel replacement safe to DIY. Not that there's anything wrong with a QO panel! It is small for my tastes.
However I think you definitely do have a split-bus "rule of six" panel.
Fill the empty hole in slot 28 with a spare breaker. They make proper blanking plates, but I find them flimsy and expensive, and breakers are cheap and a heck of a lot easier to find. Label it N/C.
The zinc plated copper ground wire is fine. You can't use aluminum for ground wires.
The big aluminum is fine and in fact preferable, since the lugs are aluminum. Beware of small gauge (12-8 gauge) aluminum wire in the house on branch circuits. That is the scary stuff. Until recently, the repair approach was to run around screaming and tear your hair out, then tear your wire out. Today, there's a magic device called an AFCI breaker which will catch arc faults, which is what we're worried about with aluminum wire. That, with CO-ALR terminations or Alumiconns, I'd sleep well at night.
It's definitely a Rule-of-Six "split bus" panel.
Now, the dead giveaway of a Rule-of-Six panel, look at the top 12 spaces (where the six Rule-of-Six 2-pole breakers go). Follow all their wires. Are they all accounted for? NO. Breaker 1's extra fat wires do not leave the panel.
Its top wire does a most unlikely thing, that seems like an optical illusion but is not: it goes straight down, just to the left of the L1 lug. Look close in empty position 9, you can see it again just left of the bus, with that same spackle splattered on it. And just to the right of the L2 lug is an equally fat wire that is mostly obscured, that can only be its partner. Split-bus panel.
Now look at Space 14, right side. Compare to spaces 28 and 30. See how the bus is different there, as in weirdly missing? Split-bus.
I'm not a fan. I would transform any Rule-of-Six panel into a Rule-of-One panel by having only one breaker in the Rule of Six area. QO makes snap-on breakers as large as 200A that will fit there, then I'd feed an external subpanel. (the internal subpanel is too small).
** If you really know what you're doing, you can activate certain loads, e.g. 240V-only loads (which have no neutral).
Best Answer
You have an old "BX cable" installation. This was common 100 years ago they ran "flexible armored cable" in homes - quite often in conjunction with "knob and tube" wiring. There were NO separate "safety grounds" at the time. The panels DID NOT HAVE a separate "safety ground" bus panel. "Safety grounding" was SOMETIMES done at the meter panel, then a metal tube ran from the meter to the breaker box, supposedly providing a ground path, and then the supposedly grounded panel box itself provided a ground through the BX armor on the wires assuming the correct metal clamps were used on the jacket of the BX cable where it entered into the panel. Sometimes they would run a "ground" wire from the panel to a cold water pipe.
The CORRECT WAY to have electrical outlets in this setup was to have UNGROUNDED outlets WITHOUT a ground prong. Of course this would require using the "cheater" 3-into-2 with a dangling ground wire things everywhere. But at least the user plugging anything in would know the system was ungrounded and could either buy double-insulated appliances or take their chances.
"back in the day" people would sometimes drill holes in these panels and install a separate ground bus and ground wires assuming space existed in the breaker panel. Yours certainly does not have enough space for this IMHO. I personally would question if all those breakers in there would even trip at all they are so old. Plus you do NOT have a proper main disconnect breaker.
If this was mine I would demolish the main panel and buy a modern one with modern safety "smart" breakers in it. Your incoming cabling from the meter also looks like possibly a 100amp (or maybe lower) service and I would suspect the thing is already overloaded so demolish all that and replace with a proper modern feed from the meter. Those old 2 wire systems are safety hazards and at the least, doing it this way will give you some GFCI/AFCI protection and with an old wiring system like that, plus given the tampering it has likely suffered over the years, that would be the wise choice.
Look at it this way - you are already saving a ton of money installing your own mini-split, well I would rather be safe from electrocution in my own home than cool so take that savings and spend it on a main panel replacement. Yes I know you are looking for a quick answer here but there is none. There is NO safe way of "modifying" this installation to make it safer with ground wires and whatnot and the second you touch the panel like that you are required by law to follow code and there's no jurisdiction out there that would allow a panel like this to remain and meet code.