I've done epoxy through a needle, and it is rather challenging. Heating it up might help, but make sure you have an epoxy with a very long set time, because the heat will make it set faster. Also keep a bottle of acetone nearby, because that'll keep the needle clean. Also helps to run a bit of acetone through it before you do the glue.
The handle that popped on me did end up popping again, despite the glue. So, I wrapped it heavily at the fades with some thread (which did give it a nice look also), and that sort of fixed it. It still opens at full draw (but do keep in mind that this was a 35# bow, so not sure how it would work for higher weights), but I don't think there's any chance of the split spreading.