Since one grain of desiccated thyroid med is equivalent to about 66 mcg of T4, your old dose of 113.75 mg of NatureThroid (1 3/4 grains) was the equivalent of about 116 mcg of T4 (1.75 times 66 =115.5). T3 is about three times as potent as T4, so your current dose of 88 mcg of Synthroid and 20 mcg of T3 is equivalent to 148 mcg of T4 (88 + 3 times 20 = 148). So with that dose increase you are feeling better; however, it increased your T4 from about 68 to 88, which is the wrong direction when having high RT3.
To switch to NatureThroid plus T3, I think the best dose would be 1 1/2 grains of NatureThroid plus 10 mcg of T3. This would give you 58.5 mcg of T4 and about 23 mcg of T3, which is equivalent to about 127.5 mcg of T4, which is an increase from your original 1 3/4 grain dose of NatureThroid, but not as much as your current 88 plus 20 doses.
When you said that trying ot raise NatureThroid exclusively showed signs of over-medication, did you mean a suppressed TSH or did you have hyper symptoms?