Altering the cooling by replacing a non working thermo will undoubtedly make a difference as clearly the engine was designed to work with the existing thermostat working properly..
However, modifying the rad could be both time consuming and expensive, and may ultimately produce no better results than blocking part of the existing rad off with a piece of flat plastic..
Testing our theories is the hurdle, unless that's done we can waffle on about this forever. And personally, I don't think it's worth the risks involved..
...