sounds a bit of a nightmare
full linux clients at scale is difficult. and as prev post said consultant lock in.
*build a smartcard interface for browser (may require plugin)
*move all core applications to web model
*use net booting thick clients with guest login or kiosks but either way running the browser as a local app - load these with ram (like 16gb)
*add second or third monitors so users are 'getting something' and have added productivity
also prob work ok with byod with ur 'smartcard plugin' but firewall these devices off with something like zscaler or similar
accept there will be technical equipment that falls under different scope.... mri machine needs windows or similar. treat these as special cases that require extra attention.
have a nice day