Not all digitals have the same key spacings or key widths. I don't have fat fingers but did have more trouble with Roland due to the height, angles and edges of the keys, than with Kawai or Yamaha. So if the DIY mod doesn't work, or ruins your instrument, the advice is indeed shop around.

Or, Wicki-Hayden.

1) have you tried taping the offending fingers temporarily while playing to slim them down(sort of like Michael Jackson)
2) using talcum powder on the fingers to facilitate the sliding in process.
3) trying to slide in between the black keys BUT not from the top directly down, but slightly pushing forward thus reducing the friction that causes the neighbouring black keys to be pushed down too.

maybe combining 2+3

let us know if any of those suggestions help

Haven`t tried the tape bit! But my last Kawai was Ok, I played better on it. Only sold it cos it was heavy for gigging . . . I have to play a bit differntly now; I get by. But I`d sure like it better! (Wiout having to buy a Kawai . . )