I am sorry to hear you are suffering. Unfortunately, many women report heavier periods after tubals. By "cauterize more so my period wouldn't be as heavy" I assume you mean endometrial ablation (cauterizing of the uterine lining). Ablation can cause problems because the ovaries continue to tell the lining to build. But the scarring of the lining causes the blood to get trapped in the uterus. Another thing that can happen is that the procedure can cause scarring of the cervix (stenosis) which can also prevent blood from escaping. This can cause painful cramping and general pelvic pain.
A periodic procedure to insert a stent and allow the blood to escape can be helpful if the cause is cervical stenosis. I have read of women finding a supplement "cocktail" to relieve the pain but do not recall the specifics. Another option would be to take birth control pills which prevent ovulation which should prevent the lining from building even though you do not need them for their intended purpose (birth control). Also, sometimes periods stop completely for awhile but then start back up on their own. This may bring relief from the pain.
I hope this helps!