Chris, you can't hone to +20 it has to be bored.
G'day folks,
Norm, honing is actually the B&S specified procedure for doing bore oversizes up to 0.020"!
See B&S Service Manual P/No CE8069, Section 9. They do strongly recommend setting the job up on a drill press, and require the use of a good quality 3-stone hone, though.
Would another option be to hone the bore, reuse the same piston and clean the scratches up on the piston and try get some new rings to suit?
To clean up that scoring properly, you'd have to remove a significant amount of metal. Which most likely will take it up to .010" oversize or more, and preclude re-use of the piston.
There are a few options here, and parts cost very much comes into play.
Option 1 is to hone it to oversize, and fit a new oversize piston kit. As AVB says, 0.010" OS piston kits are NLA through the trade, but New Old Stock [NOS] ones are still around, in the US. FleaBay US is the best place to look, as you can see at once if the seller will ship internationally, and the estimated shipping cost if they will. Many US parts shops won't ship outside the US, but it can take a bit of digging on their websites to find this out. Shipping can get exy, too.
The P/No for those is 295588, and a search on FleaBay US brings up a cheapest option that will cost around AU$85 delivered. For comparison, a new standard piston kit #295587 is $147.49 + postage from the ODK Shop [genuine B&S]. 0.020" oversize is in the same ballpark.
Option 2 is to give it a very light hone, clean up the piston a bit, and fit a new standard ring set. The ODK Shop has #294232 ring sets for $42.21 aftermarket or $82.15 genuine.
Option 3 is as for 2, and fit a new standard Chrome ring set, #297201. Once more, these are only available as NOS; the advantage is that Briggs' chrome rings can tolerate up to 0.005" oversize bore. FleaBay US cheapest is ~AU$40 delivered.
In addition, you'll need a full gasket set #297275, and I'd strongly recommend replacing the crankshaft oil seals.