He's right you know.
These are make of cheese - I've had issues myself and my bike shop has too. for a while the part was unavailable which says a lot...
I removed mine by using a Tx bit just a fraction larger. Grind or stone the end flat so it is 'sharp' and push it into the socket, then turn it while keeping the bit pushed into the socket. Mine broke free reasonably easily using this method.
SJS had some is stock a month back, I'd try them first.
In the future don't do them up very tight, use a high quality hex key (something like a Wera HexPlus or Bondhus) to remove them and maybe pray to your favorite deity.
It really is a poor bit of design from Shimano. I suspect it was done to limit the force used to do these caps up, but doesn't seem to have accounted for the caps binding in place and the increased force needed to undo them!
For small Allen sizes ( 2mm and below) always best to use ...https://www.halfords.com/workshop-tools ... er-bit-set
Providing you have room .