Any possibility you could switch to an 6 speed freewheel? It would be a tight squeeze but maybe a possibility. Shimano currently makes the Tourney model in a 14-34 6 speed freewheel. You might have to buy it on eBay from China to get a reasonable price. Tourney is a fairly low end product but most of these are used on new entry level bikes so that's what is out there. It looks like the difference may be as little as 6 mm with 6 and 7 speeds the same for road bikes according to the Sheldon Brown website.
https://www.sheldonbrown.com/cribsheet-spacing.html