If I'm remembering a real thing, I remember one guy on an email list that made it work, sorta, using an SR rear derailleur, a floating upper pulley, a Shimano SIS freewheel, and a Suntour Accushift lever, or some sort of weirdo kit bash like that.
Maybe there were Syncro I inserts for SR derailleurs? Again, may be false memory, and even if they existed, you can't find one, and even if you did, that little piece of plastic would be like 300 bucks and wouldn't work.
Bottom line, the OP needs a new rear derailleur. (Or Simplex retrofriction levers, with their micro-tiny cable pull and general awesomeness.)
--Shannon