OK, I missed the OP's second post.

I don't disagree with anything that's been suggested, but the easiest depends on what is available to you. One option would be to find a set of old but serviceable wheels in the same size at a coop or something. The other option would be to use a new set of wheels from velomine or something in 126. You'd need to spread the frame slightly, as has been said. For the latter, an easily available standard 6 or 7 speed freewheel could be used, though 7 might require an extra washer, as the spacing can get tight.

If you go to 700c keep in mind they are 4mm smaller in radius than 27", and brakes need to have 4mm of adjustment room.

I wouldn't get too fancy with a Mirage or Nomade. They were entry level bikes.