From just looking at the pictures, it appears you have some pretty good pits and scoring in other cylinders. Also, I can see evidence of corrosion on some of the piston tops - which usually means there was moisture in the cylinders at some point.
Since you have to take it apart anyway, I'd have the machine shop inspect ALL 8 sleeves and potentially replace them all, hone them and put new rings in the engine. Also, there could easily be some rust/pitting on the valves/seats . . . so I'd probably have them touched up as well. Also, when you have rust/debris that scores cylinder walls a lot of times it gets into the oil and scores the bearings.
This is how it usually goes for me . . . every time I think I'm going to get away with a few "band aids", I end up finding more issues. So, I then make the decision to do the job the right way and rebuild the engine. While I don't like to spend the money, I also hate to spend all the time and put the effort in and not have the best result possible.
I'd take it all apart and have everything inspected by a machine shop that knows flatheads.
I'd also be mentally prepared to rebuild the engine. You'll then have a really good running engine that should last the rest of your lifetime. Not trying to spend your money - just trying to be realistic and pragmatic.
Best of luck and welcome to Flatheads - they are fun engines!
B&S