I'm skeptical of that CC reading of 10.

Try your CYA test using the disappearing black dot test instead of strips. You'll have to dilute the sample to get a reading. Take one part pool water and one part distilled water. Mix and then run the test on that. Multiply your result by 2. If you still show a reading of 100 with that, do it again but this time take one part pool water and two parts distilled. Multiply the result by 3. This dilution method won't be super accurate, but will at least get us a better ballpark reading of what your CYA actually is. At any rate -- no more trichlor pucks or dichlor shock powder in your pool!

What is your calcium hardness reading, by the way?

You are right that a 10ppm difference in your TA results is insignificant. But, your alk is to high. Please read the following two guides:

Lowering Alkalinity Step-by-Step

Using Muriatic Acid Safely

Yes, you will have to keep your chlorine high. Please read the Best Guess Chlorine Chart in my signature below. Also, with such a high CYA pool, you are going to have to have the K-2006 kit. The other kits are not going to be able to read the high chlorine levels you are going to have to run. Test kit page in my signature above.