If you lower your TA to about 80 ppm when using bleach or ANY unstabilized chlorine source then you will find that your pH would be stable. Your TA was too high! The MAIN cause of pH rise in swimming pools is from outgassing of CO2. By lowering TA your slow the outgassing and the pH rise. Tabs are very acidic so, in effect, you are adding chlorine, stabilizer, and acid all at once. The constant acid addition causes TA to drop so you have to set the TA higher then when you are using an unstabilized chlorine source. Unstabilized chlorine sources, inscluding bleach, are basically pH neutral. The are alkaline when added but the reduction of hypochorite to chloride (which is what happens when the chlorine is 'used up') is an acidic reaction so the net effect is pH neutral. Trichlor and dichlor (the two stabilized chlorine sources used in pools) are acidic when added (trichlor quite acidic in fact) and the same acidic reaction takes place when the chlorine is consumed so the net effect of use is acidic. This means you never need to add acid but you do need to monitor TA and pH closely and adjust as needed and maintain the TA at a higher level so it will drive the pH upward faster to compensate for the 'acid' added by the trichlor.

If you were adding 9 (96 oz) bottles of 6% bleach per week then you were adding about 28 ppm FC weekly. This is a 4 ppm FC loss per day which I find hard to believe with 60 ppm CYA in the water. It means you were fighting some sort of algae bloom that would have been quickly taken care of by just shocking the pool.
On the other hand your 4 (8.3 oz) trichlor tablets would mean you are adding only 15 ppm FC weekly, about half of what you were supposedly adding in bleach but you are also raisng the CYA by 9 ppm weekly and dropping the pH by .8!!!! (That is a lot of acid!).

The numbers just do not add up so I would have to say your experiment is a failure either because of inaccurate testing, improper dosing, or some other error on your part. It has been documented time and again that bleach is more cost effective than trichlor.

If you added bleach and the FC did not rise I would suspect a nascent algae bloom or something growing in a hidden area of the pool. Your chlorine demand was just too high to be normal. I also find it hard to believe that there were no problem when you added half the amount of chlorine with trichlor weekly since you were causing the CYA to rise once again.