Alright here is the solution, after some testing. Display settings does in fact "fix" it, but it's a imperfect solution.
Go to settings > display > advanced > display size and select "largest".
Strangely, that makes DS run in full screen without the software buttons.
It makes your phone look terrible, so you'll probably have to toggle it each time you play.
It also introduces a couple other visual bugs, although none of them are as bad as not being able to use the right side of the screen.
Also worth noting, selecting "smallest" exaggerates the problem and makes the game even more unplayable than I previously experienced, with far more buttons (such as the raid fast forward button) being unreachable.