Electrical – No grounding wire in an old house

OK first of all you cannot determine whether the box is properly grounded just using a multimeter. The fact that it reads "0V" does not mean it is properly grounded. The only way to determine that would be to confirm that there is a proper ground wire all the way back to the panel, or to confirm that grounded armored cable is used. In your case I would just forget about the ground and disconnect it, you don't need a ground for a GFCI.

Second, try to get the GFCI outlet working without the downstream outlets hooked up to the LOAD side. If you can get the GFCI working by itself but it trips when you hook up the downstream wires, that probably means there is something downstream creating a ground fault and the GFCI is tripping (as it's supposed to). A common cause might be a neutral wire touching a metallic box or a "bootleg ground" where neutral and ground are connected.

If the GFCI doesn't work even on its own, it's probably defective.

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.