I think just having the SA7 pickup kit spawn somewhere obvious at Lower Town would do the trick. It's a critical part of UKR defense, but right now it's more of an easter egg since nobody knows where it is (not many spawn at the back flag). Other than that, I think the map's perfect - definitely my favorite PoE2 map. The asymmetry is so refreshing.
I do not want to do that out of fear of them losing that flag which is when they will need the AA the most.
...except that 95% of the time the Shilka would spend it's time raping flags/infantry
If it's doing that, then the cobra wins. It would put more emphasis on the Arty covering the landings as opposed to the cobra doing all the work. Remember, my issues with this map are early game. As in my experience the round is decided early game. I think a shilka could force a little more restraint from the Cobra allowing an inexperienced team to do battle against an experienced team which is often the case. Say what you want, right now the cobra can do what it wills until it takes a hit or 2 from SA-7. Then off for repairs.
Shilka would rape flags and just be way to much AA in my opinion. As a defender, the cobra really is not an issue to me. I use the Sa7, Zu23, or the Dozer to bring it down without issue. Heck, even the T84 is a great AA weapon on this map with the heightmap.
I have made some other changes to the overall map which I feel addresses this issue however I found it odd that 32 player static AA is not helpful combined with the Sa7 on that map. While the Ukraine team takes a beating from arty and cobra, the USMC has less options to get boots on the ground and cant take the popular side path to the church and back flags (Which wont be as easy in the next version anyway).