FAL is not any good on close range maps just for the reason you are saying, the game gives a "lag advantage" to SMG's at close range. I have the same problem. If two guys pull the trigger at the same time and are staning 5-10 feet away, the SMG wins every time. Even if you get a headshot on your end. If you need better close range weapon I would try akimbo on semi-auto pistols or do the warlord perk (is that the right one) where you have jitter on a shotgun as a secondary weapon. Yes, you'll have to remember to turn it on and off.
When I play short range maps, I don't double up on weapons (no need). I either just run around suicide style with akimbo pistols or jitter shotgun and I still get top kills and best kdr on maps.