More work has been done for JPCSP's full-screen mode in r2097. This is still very experimental, so it's somewhat hidden to avoid misusage, for now.
If you still wish to give it a try and enable full-screen exclusive mode in JPCSP, there's now an additional option under Configuration > General that when checked will lauch JPCSP in full-screen on the following runs. However, this will launch a completely undecorated grey window, so there won't be much you can do there.
The trick is to press F4 to switch back to a normal sized, with menus but no borders, window (a bit hackish, I know
). There, you can load and run your game and press F4 again to switch back to full-screen. Of course, this is only possible when starting JPCSP in full-screen from the beggining. Also, this time, full-screen is really changing the screen's resolution. 
The goal will be to come up with a way to get rid of the unecessary switches each time you want to load a different game, but, again, Java doesn't really help here...
If you still wish to give it a try and enable full-screen exclusive mode in JPCSP, there's now an additional option under Configuration > General that when checked will lauch JPCSP in full-screen on the following runs. However, this will launch a completely undecorated grey window, so there won't be much you can do there.
The trick is to press F4 to switch back to a normal sized, with menus but no borders, window (a bit hackish, I know
). There, you can load and run your game and press F4 again to switch back to full-screen. Of course, this is only possible when starting JPCSP in full-screen from the beggining. Also, this time, full-screen is really changing the screen's resolution. The goal will be to come up with a way to get rid of the unecessary switches each time you want to load a different game, but, again, Java doesn't really help here...