You most definitely can, and you most definitely will get a different sound. You will have to specify the exact turns ratio to Jack Elliano so he can custom wind you a transformer. Of course, it may or may not fit on the same circuit board that was designed for the Hammond. The output transformer is the crux of any amplifier. In a parafeed preamp,the output capacitor is as well. The bypass cap will make a difference too. See my gallery for the parafeed preamp I built years ago for ideas if you want to diy on your own. FWIW, Jim's design hits the price/performance value quite nicely. However, If you can stretch your budget the sky is the limit. If I were upgrading, I would change each of these items one at a time. The output transformer first, next the parafeed cap, next the bypass cap.
Best,
Anand.