The lawnmower piece looks like it might do the job, would you replace the spring with a threaded bar to make it more... 'manly'?

Been trawling the parts catalogue too, seem bikes don't use belts, but have you seen the wheel tug/aligner/things?
https://www.ebay.co.uk/itm/PAIR-of-Y...4AAOSwcUBYUC4R
perhaps not the most elegant solution, but they can be had (or made) cheaper than those, just a shame that it makes the actual mounting a tad more awkward.

Just while I'm thinking, single speed bikes have tensioner parts for chain slack, I doubt they'd be tough enough, but if you can make your own beefier ones it might do the trick?