Looks like it could be a good project. The bmx freewheel will thread right on. A couple of concerns though, make sure the threads on that are English and not the Nottingham one, two You may want to go to front chainring in the 40's instead of the 39. It's quite easy to spin out at 39/16 with the 27/700c wheelsize.
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Appreciate the old bikes more than the new.