Years ago when belly putters became popular as a winter project I tried the concept altering some old putters I had in the bin. I discovered some common factors that seem to apply to all. If the putter head is too light I had directional issues. If too heavy I had distance issues. Also, I found that gripping the putter higher or lower had and effect on both as did putter length. So, basically you have to experiment with all factors and hope to luck into a total combo that works for you. What works best for me is a 41" putter with a 430g headweight. Yes, it is still a belly putter, f' the USGA. I have used the same Mentorsports Triad II putter for probably 10 or more years. The head has three 1/2" x 2" round weight ports and lets you try a huge amount of weight combos.
Chuck if I were you I would try lengthening your putter to 35 or 36 inches and try that. Putters don't really have a swing weight but at longer lengths the head will feel heavier. Also if you are playing a center shafted putter or a faced balanced one, you might try a heal shafted or a "toe hanger."