Interesting. Have done several low budget 6 to 7 speed freewheel conversions (with friction, indexed, or STI shifters). Often need to make space for that 7th cog. Use some cone wrenches and move a washer from the non-drive side of the axle to the drive side, re-center the bearings on the axle (getting the drive side very tight, then doing final bearing adjustments on the non-drive side), re-dish the wheel by adjusting the spokes a small amount (maybe 1/4 of a turn tighter on the drive side, loosen spokes by the same amount on the non-drive side).

But too much dish is a bad thing. And freewheels hubs have an built-in issue, the drive side bearings are close to the center of the axle = bent or broken axles (larger riders beware). If you like the frame, want to ride it allot, and would not mind spending money, you could load up on newer components: cassette hub for 8 9 or 10 speed gearing, new cranks/rings (triple or compact), new chain, new derailleurs, possibly "brifters". One of my rebuilt bikes retained only the original frame, fork, headset, and rear brake.

Keep your existing cranks:
Budget option parts costs about $25 for a chain and a 13t-32t 7 speed freewheel. Keep your existing cranks-rings & derailleur. If your derailleur can take up as much slack chain as a short cage Dura Ace or 105 racing derailleur it will work ok with a 13t-32t 7 speed freewheel on 52t/42t chainrings.
Mountain cage rear on a 52t/42t front? Not needed for a 13t-32t. Not much gained with a 13t-34t. Good option though if you change the crank to a triple or compact.

Had only known of the 11t Shimano freewheels. Just stumbled on those other brands of 11 speed freewheels with a quick google search. See some results with various terms, like "13-32 freewheel". Would rather have Shimano quality, but the cheap ones have worked for me, and the rudimentary shift ramps on the cogs make them shift better than old plain cogs, or twist tooth cogs.