Considering the purchase price, you still have room to replace the whole engine and break even. I'd start by measuring the cylinder to see what you really have. The main difference between the MS290/310/390 is the bore diameter. Crankshaft and connecting rod are the same. You can reuse them if they pass inspection.
MS290 is 46 mm bore
MS390 is 49 mm bore
The 310 is somewhere in between.
I would not put this saw back together as a MS290. 390 or bust! If you order a 390 top end, you can simply plug the port for the decomp valve since you don't have the plastics to accommodate it.
I did a 390 with an aftermarket kit not too long ago, came out great!