It will depend on the membrane type if there's a way to change the wiring layout.
Since you can't really add diodes to a membrane (as far as I know), some boards use what's called a 6+2 or modified nkey rollover, lots of various names and layouts but the gist is that instead of "2", "W", "S", and "C" being on the 3rd column they move "W" over to a different or even extra column. Same for "A", "S", "D", they move "A" to the top row (not exact, this is just an example). Basically they break them up into completely different column/rows from other commonly pressed keys allowing the controller to more easily identify them. Doing this means that you either software to remap keys when done but it's also dependent on being able to modify the membrane and the controller being able to handle it (being an office keyboard it's unlikely and the only way to fix that is a new controller).
Personally, given the amount of effort this requires, along with tools and such, and the minimal chance of it working once all is done, I wouldn't bother.
That said,
A big part of your problem is your use of Caps Lock, as mentioned about A,S,D, being on one row, you're compounding the problem by adding a 4th key to the mix. Pick a key on a different row/column and you might fix your problem.