Thanks for those clarifications, FAST GRASS. It sounds as if the marks in the bore were due to the aluminium grabbing the hone despite the kerosene, not to anything you did that I might not have done. My guess would be that your hone applied too much surface pressure to the aluminium, which seems quite likely if it is designed for use on a cast iron bore. This may help to explain why Briggs advise against breaking the glaze in an aluminium bore.

Unless the rings fail to seal against the bore, it should last fairly well, and be quite OK except for some slight additional piston slap, which hardly matters on a ride-on. You'll probably achieve quite reasonable ring gaps, based on the bore size measurements.

So far as affordable Tecumseh parts are concerned, you might try the US vendor Mr. Bonnar used in this thread:

https://www.outdoorking-forum.com.au/forum/ubbthreads.php?ubb=showflat&Number=38144&page=1

My recollection is that the prices he paid for his Lauson parts were reasonable. Incidentally the Honda rings I use are $15 including shipping for "basic" Thailand ones (to Honda's original design except no chrome on the top ring), and they would be $19.50 including shipping if I wanted chromed rings with steel rail oil rings, from Honda's Japanese original equipment vendor.

I'll leave this thread open, for you to post progress reports - which I for one look forward to reading.