I'm going to jump in before Simon!
Going upwind is easy once you get the swing of it...maybe you need to tweak your technique, as the JP may not be as forgiving as your other board. A bigger fin helps, but even with a small wave fin on a wave board, you should still be able to go upwind once you're planing...
You want to be reasonably powered up - more so the better. The idea is to move your weight forward, and still keeping pressure on the fin, swing forwards towards the mast in the harness.
When you head up wind, change direction slowly at first, and get a feel for the change in balance on the board. If you turn too sharp & quick before you get the hang of it, the board will stall.
So start turning upwind slowly, and at the same time swing forward to put more of your weight towards the front of the board .. sort of like trying to push the mast foot down if you will.. try and keep the mast vertical - don't pull it over your head, or you'll kill the sail area you need...
Keep the board flat, or if you've got sharp rails, you can try tilting the board away from you - the far side of the board can be used to edge into the water for better upwind 'grip'
Somethin like that .. then you can bear away for a downwind bit, then upwind - good way to get a feel of where your body should be in relation to the sail...
Hope that helps...
Have Fun!!! .. Laurie