Joysticks belong between your legs, period.

For one thing you have a much better range of motion and control than at arms length on your desktop. For another you can "brace" your arm on your leg, for very precise control, can't do that on desktop.
But there is one other option that also works very well.
Take a board or piece of plywood aprox the same size as your joystick. Screw another board to it so it looks like a T. The upright should be aprox 5" tall and about the same length. The lower leg of the T goes between your legs. You can even split one of those foam swim noodles, and pad the lower part of it.
Then attach the stick via velcro, tape, screws, whatever to the top board.
My buddy tank1 built his this way, then cut out the top board to match the base of of joystick. A couple of carefully planned holes and a couple of sheet rock screws locks it down nicely. Drop it into position, the legs hold it rock steady.
its up just a bit higher than between the legs so you have even better range of motion. Control is in my opinion much better than on the desktop.
Probably not going to work as well for a full hotas setup as a single twisty stick. But its something to consider.
If anyone is seriously interested in this I'm sure tank1 or I can come up with some pictures and help.