I googled for apps2SD for LG Ally (the other name for Apex), and there are references to the fact that it can be done and has been done all over the place. Took a little while, but I think I found it. (Funny enough, it came from one of our own moderators, Trident.)
Now I am not sure if a rom designed for the LG Ally would work on a Apex or not. The two are variants of the same phone, but that does not necessarily mean that the rom will work on both phones. E.g. Galaxy S I9000 roms do not work on the Galaxy S I9000M. So do this at your own risk (or just ask Trident. He might have an answer).