Yep,
"there's a little button you may push to swap the datum from HPa to inHg and back, and another one to turn feet into metres"
As I said, most modern EFIS aircraft can do this. I've never flown with a Garmin G1000 cockpit but I'd be surprised if it can't do it too! So that means even a 172 has that capability!!
"getting it in one set of units and having to do the conversion "on the fly" would be a pain"
It's not too much of a pain. You know you're going to have to do it so you have the conversion table ready to go. Get the new pressure setting from the Controller and read it back as he said it, then write it down. Get the table out and make the conversion. If it's a two pilot operation then both pilots convert independently and confirm before setting the new datum. If its a single pilot show then just take care and cross check it yourself before relying on it.
As pains in the ass go it's one I can live with fairly easily.
3 Point