Maybe it can be improved, but it's not a simulation... we'll think of something eventually...
It works when you put the setting to no because it's back to what there was for the sdl-1.2 version : the d-pad totally separated from the sticks, that's also why after that you need to reassign it in the inputs if you want to use the d-pad. But the gui accepts movement from everywhere : the left stick, the right one, or the d-pad ! So your problems are back for good, the move is canceled again here. Well as long as the sticks are not used for analog inputs maybe the dead zone can be increased... Not sure about that, I'll try to borrow a ds4 controller to see how it behaves in windows... I thought 2500 was already very big for a dead zone, it's quite scary that this thing needs something bigger, for me everything works perfectly here with these settings (ok I almost never play in windows...). For now you can always use the stick or the keyboard, autorepeat works with the sticks too, or use the keyboard it's way faster to control the gui !
There were much worse cases with the sdl-1.2 version, that was the main reason for upgrading to sdl2, and I delayed it as much as possible.
Here I can't reproduce it for now, and it's easy to work around, you don't switch from windowed to fullscreen all the time if you save your settings, and when it happens just press esc to call the gui and have everything back to normal, so it's manageable. If you want to test, the other rendering option "sdl2 native" probably doesn't have this problem, but yeah it has a lot less settings too !