Hi Hemmjo
Wow sure made a mess of that engine.
Unfortunately any form of purely circular lapping will always leave a grooved finish due to trapped debris and media, but you can certainly remove metal to a point. You could try gluing thin strips of emery radially to get over the wrinkling, that may help to give the debris somewhere to go, after that for me it would be down to hand finishing, a mirror finish is not necessary or even desirable, just smooth. Now I know what machinery you have, after finishing the chamber you could machine the squish band using an angle plate on the lathe crosslide and a boring head.
Click image for larger version.  Name: angle plate.jpg  Views: 470  Size: 263.9 KB  ID: 18743
I have done more than a few jobs in this fashion using my drill table as a large angle plate.
The only problem I can see then is balancing the combustion chamber volume, you can do this using a measuring burette and paraffin but it takes a long time.
You seem determined so I am sure you will end up with a usable engine.