You don't have to "cold-set" the frame to slip a 130mm 8,9,10 spaced rear wheel into your frame. All that is required (if at all), is slight outward/spread with your fingers when installing a 130mm rear wheel.

Have you/did you try adjusting the travel limiting screws on the front derailleur? Sounds to me like at least one travel limiter screw is not adjusted correctly (travel limiter screws keep the front derailleur from traveling too far inward (on the small chain ring), and too far outward (on the big chain ring).

Converting to 8, 9, 10, speeds on the rear wheel will require a replacement rear wheel (8, 9, 10 speed rear wheels use a same size freehub, change to one of these will require a new wheel), shifters (buy shifters to match the number of speeds on the rear wheel), rear cassette (buy to match shifters), and probably a chain (8-speeds uses a chain with the same size links as 7-speeds, but the length required may be different, 9, and 10 speeds use different chains with different size links, and switching will require a new chain).


You may need to replace the crankset (if changing to 9 or 10 speeds), as the distance between the chain rings is narrower on 9 and 10 speeds, and the new 9 or 10 speed chain may fall/jam in the space between the chain rings.

You might also need to replace/upgrade the shift housings and inner cables to get shifting to work properly.

The change to 8 speeds in the rear is simpler, because the chain link size is the same as 7-speeds, and the derailleurs, and crankset will still work. Only parts that you need are the shifters, rear cassette, and a rear wheel, OR a replacement freehub body for the rear wheel, if the existing rear wheel with take a longer freehub. Since you are having problems with your rear wheel, and need to replace it anyway, this would be a perfect time to change/upgrade to 8-speeds, since it is a minimal change at minimal cost.

Look on your local Craigslist for shifters and a set of rear wheels, or for a bike being parted out that you could take what you need from.