So looking at members if we want to yellow light someone I would suggest Rigellans and Tellarites. Both could spare an Explorer and the Megatortoise has 9 shield and 8 hull to go with 6 combat, though if they send that I would recommend a tortoise as escort as their escort class ships are fragile. Tellarites have an excelsior and Connie b and could send one of them with two Miranda-A as escorts
Hm, looking at our members:
The Caitians are the strongest remaining uncommitted member with 20 ships containing 65C, 89L, 28H. I have to wonder if they might not want to get particularly involved in the GBZ though, given how far away they are from the zone and the Orion situation. Also the Dawiar are right there on their border.
The Rigellians are next with 16 ships containing 48C, 57L, 47H. Like you said they are a good choice for another member to activate. Of course, there might be some reluctance on their part for the same reason as the Caitians, they are pretty far away from the GBZ. Plus, have plenty of open space to expand into nearby.
Interestingly, the Indorians might be a very good choice because they have 15 ships containing 50C, 39L, 25H. Looking at nix's maps, they actually seem like they might be pretty open to helping given they're butting up against several other groups, and they are closer than most other choices.
Next, the Tellarites have 11 ships containing 37C, 30L, 23H. Given their limited ship numbers, if we activate them we probably want to activate another member that they can combine forces with, or we want to only yellow light them so that they are working alongside starfleet ships.
Vulcan is the last member we can really activate for reasons I'll get to in a moment, anyway they have 12 ships containing 34C, 26L, 19H. They are definitely our weakest choice however, because assuming your sheet is right one of those escorts is an Oberth, two are ancient Soyuz class ships, and three of the rest are plain Miranda's.
Of our remaining members, United Earth and Andor are currently heavily committed to the Orion situation and thus rather unlikely to give much if any help. The Betazoids on the other hand both do not have much in the way of forces and are pretty much as far away as possible from the GBZ. It also seems likely that their forces are at least somewhat committed to making up for United Earth's comparative lack of presence in Sol sector. (United Earth only has an Excelsior, Constitution-B, and Constellation left, I think?, which is a lot less than everybody else expect the Andorians)
Edit: Corrected Indorian total combat value.