I tried everything, uninstalling and reinstalling GSX, Addon Manager, these things you described above, nothing worked.
Reinstalling GSX or the Addon Manager won't fix this. If it could, I would have suggested to do so.
It's not very clear from your message, if pushback at the airports you tried used to work before, or they never work in the first place. If they used to work, the solution would be the one I already explained: refreshing the cache, to be sure it's current.
If they never worked, maybe the problem is entirely different, and it's just the issue of the scenery developer setting the Pushback preference to "NONE". In that case, it's NORMAL you would only see the Straight pushback option.
This is of course fully explained in the GSX manual, and can be overridden in GSX, setting a pushback direction for the affected parking in the GSX parking customization page.