These are the mounting plate dimensions for the two sticks:
Mag Stick:
JLW/U360:
As you can see the Mag Stick mounting hole dimensions are 76x46.5mm. The effective mounting dimensions of the JLW/U360 are 85x50mm.
While they are not an exact match you could probably enlarge the holes in the U360 mounting plate so that you can use your existing fittings. The U360 mounting plate has small 5mm wide mounting slots so I would imagine you would have to enlarge them anyway as I presume your mounting hardware for your Mag Sticks is larger than 5mm. As long as you use a decent size washer on the enlarged mounting hole I think you would be fine.
The U360 also has a very slightly larger mounting plate (97x65mm vs the Mag Sticks 95.4x63.3mm). If you have recessed your joysticks you will need a slightly bigger recess but I would imagine they will fit in unless your were very precise with the pocket dimensions.
If you like I could overlay the mounting plates on top of each other in AutoCAD so you can see where the holes line up? I'll have a look for you when I get home from work later.