My view is that 'inched' and 'inch' have, by common usage, become accepted in the OP's context. I can't remember the book, but I read somewhere about a sniper who inched, millimeter by millimeter, towards cover. Does it work? Is it sloppy writing? Some might say so, but every inch, sorry, every 25.4mm x 25.4mm says it does.
Australian here. Both terms are totally used and understood in our Metric country. Our television is still dominated by American import shows, so we are more than familiar with their vernacular.
That is very re-assuring. What about The Archers? ... 'He inched millimetre by millimetre' is completely beyond the pale. I would be very depressed about reading that book. Although if you change it to 'I inched millimetre by millimetre...' it could be quite good, given context of ridiculousness, for example.
I hope it's all right, I lose sleep over spelling errors. Misspelt science once on the top of a science paper, said 'detrius' and not detritus for two years, that wasn't very clever, really wanted to be clever. Antartic/porpuse/mis-spelt/there's a few others, married to a woman who says 'panguin,' she's an idiot, describes all male behaviour as boysterous for god's sake I say, it's 'monstrous' I think you'll find, woman...
There's one pacific word, what was it? Trianctular—yes, that was it, someone I know was bitten by one. Actually—ought not to take the Michael—plenty of gaps of my own. A nudge @Scot ; can you edge?