Older Dahon. I had one - and ditched it, but that bike made me discover the world of foldingbikes.

Mine had a SA three speed hub w coasterbrake so no brake problems. That is solution number one, get a different wheel witha coasterbrake hub.

Number two: Add a rim brake to the current setup, I have a feeling that cheapo looking drum is not going to work well..

Am I right that this is the only brake on the bike (no front brake)? In that case add one there also. If the rims are steel look for different wheels from a 16" childrens bike (dumpster, yardsale or similar).