There's a way to do it with a hot plate and heat gun. Apply a special flux to the board, put the BGAs on, use the hot plate to get the board up to a preheat temperature, and the heat gun does the actual soldering. I have not actually done that with BGA, but I have done that with TSOP. BGA is definitely harder to get right and very difficult to check.
I have read stories about fixing video cards with bad solder connections using a propane torch. Surprisingly, it sometimes does work.