$80 is a lot of money to invest in an old bike. I'd hunt around for a pair of 7 speed downtube shifters. You can find them in a bike co-op; a bike shop might have an old pair lying around.

One possible downside in going from 6 to 7 is you might get some chain rub on the seat stay. 7 speed freewheels tend to be a bit wider. You can take care of that with a 1 mm spacing on the axle.

Steve's advice in post no. 3 that you need to pay attention to the rated capacity of the rear derailleur is spot on.