I flash a LOT of roms. Sometimes two or three a day. (I am going to meetings but I will always be a flashaholic.) I am almost constantly on AOSP because I do not like how clunky TW feels and there are about three or four things an AOSP rom does easily that you cannot do easily or at all on TW. I have had all of the problems you mentioned at one time or another but never all at once. When I first bought my SG4 and started flashing roms the GPS was a big issue but that problem is pretty much nonexistent now. The same with the inability to make a call. I have not seen that in awhile. I recently flashed a rom that I thought was running perfectly until I made a phone call and could not get the phone to hang up. I had to reboot to get the phone to disconnect. That was the first and only rom I have had that problem with. I think I reinstalled it a few days later after it had been updated and it worked fine.
Other things I have noticed is that Google's voice recongition does not work as well on AOSP roms and there can sometimes be a problem with MMS.
I say all of this to say that first, these roms are in development. They are not perfect. They sometimes have problems. If a rom has a glitch you cannot live with, go to a different rom.
Next, you have to follow the installation instructions to the letter. If it says to stand on one foot while installing the rom do it. I have seen some roms that have really weird install instruction but if you do not do it, the rom is not going to work. Acheron's Super S4 has you use specific recoveries and reboot into recovery. That is a little odd.
Next, if you feel you are constantly having these problems with all AOSP roms, which is odd, try flashing a stable version. CM has milestones. I know Liquid Smooth has an official 3.1 that is supposed to be very stable. See if you have these problems are more stable versions and instead of nightlys.
Next, I have seen people on the exact same model phone and carrier have greatly different experience with a rom. Individual phones seems to have their own quirks you have to learn. I believe most of this type of issue though is user error and you just don't realize you are doing something wrong.
Finally, the one thing I know nothing about is unlocking your phone for the international version. I wonder if that has anything to do with your problems.
Good luck and don't give up!