I finished the Trek 700 for my wife…well enough for her to take a short test ride. Going up a small hill, she shifted into the lowest gear, and still had difficulty getting up the hill. The largest cog on the freewheel is 28 teeth. Okay, she is not in the greatest shape either… My Trek 700 came with a Shimano Megarange freewheel and derailleur, so my had plenty of low gearing. I tried putting the old Megarange freewheel on her bike, but it was obvious that the derailleur was not made for a freewheel that big. I figured out that if I want to use a Megarange freewheel, I will have to get a Megarange derailleur. I have seen them popping up on ebay, but haven’t wanted to spend $25 for one. But yesterday there was a list for Megarange derailleur (RD-TY23) for about $5 plus $8.50 shipping. And the thing is new! Way cool! I bought one! Now I am hoping that it is a 7 speed derailleur! I know there was a 6 speed version of Megarange stuff. Some googling seems indicate this will work for either 6 speed or 7 speed.
The shifting should work fine. The deraileur is SIS and the stuff on my wife’s bike is SIS.