Yes, there's companies offering this service. DIY of course is the most secure but also the most likely to fry the chip. I'd favor those that present their work at conferences but ultimately don't envy you for having to hand your device to anybody.
Soldering on a new screen should work I would guess. Did you ask Trezor?
Trezor is exceptionally unhelpful. They won't tell me what screen exactly I need to buy at Alibaba and instead suggest to take another Trezor and remove the screen and use it - which is no easy feat. I tried soldering on a screen that I purchased but it didn't work - unclear if the screen was not compatible or if the Trezor is generally broken beyond repair.
