Grounding Electrode System
You're going to have to install a grounding electrode system. This is typically done by driving two ground rods spaced at least 6' apart, and connecting the rods together using a properly sized bonding jumper. Then you'll install a properly sized grounding electrode conductor, from one of the ground rods back to the main grounding bus in the main panel.
Bonding Water Piping
You may be able (required) to use the abandoned underground copper pipe as a grounding electrode, if it meets the criteria specified in the code. If the water is supplied to the building through metal pipe, you'll also have to bond the metal supply pipe to the grounding electrode system using a properly sized bonding jumper.
If the plumbing within the building will not be metallic, you don't have to bond it.
Bonding Gas Piping
As for bonding the gas pipe, according to the National Electrical Code, metal piping systems that are "likely to become energized" must be bonded (250.104(B)). So if you have a gas water heater that has no electrical connection, then you don't have to bond the gas piping. If you have a gas fired furnace, then it's possible that you'll have to bond the gas piping.
However, the bonding jumper only has to be sized to the rating of the circuit that is likely to energize the piping. NEC also allows you to bond the piping to the equipment grounding conductor, of the circuit that is likely to energize it. Which means the gas pipe feeding the furnace, can be bonded to the equipment grounding conductor feeding the furnace. And if the gas piping is isolated from the furnace electrical (not likely to become energized), you don't have to bond the piping at all.
In the case of the gas/electric range, again you can use the equipment grounding conductor of the circuit feeding the appliance, to bond the gas piping (if required).
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.
Best Answer
Welcome to stack exchange. This site is usually for DIY residential owners, because when you get involved in commercial you usually will need a professional electrical contractor, but I will take a crack at your question.
First your ground attached to your first means of disconnect is the building ground. It can't be a 6/0 since there is no such gauge. It is probably a 3/0 or 4/0 depending on how it was originally sized. All other grounds from your tenant panels must be sized and connected to this ground. So yes all of your tenant services need a grounding conductor to the original ground.
Second on commercial properties, if you panel grounds are mixed with your neutrals they need to be separated and installed on proper buses. Neutrals need to be on a neutral bus and grounds need to be on the ground bus, and if the panel is the first means of disconnect the neutral bus must be bonded. If you have a separate main breaker or fused disconnect the neutral must be bonded there and the neutral bus in the panel and the ground bus must be isolated from each other.
Third NEC Article 250.50 states that all grounding methods available shall be bonded together to form a grounding electrode system. I can't say how many are available on your building but there should be at least two. One is the building steel you described and two would be a driven ground rod.
Conclusion - If what you described is factual; then no your grounding system is incorrect and needs to be repaired and brought up to code. I might add that proper grounding is important not only for safety purposes, but for the proper operation of your electrical system. I can almost grantee that your tenants will have problems with there electrical and electronic equipment, and if you call in someone to trouble shoot it. It will take longer to trace out and cost more to repair.
Still I recommend that you bring in a recommended and trust worthy commercial electrical contractor to get you an "eyes on" inspection and recommendation.
Good Luck.