You need to read the Best Guess page linked in my signature, and then make a decision:

+ You can drain 75% of your water, lower your CYA, and then run 'normal' levels of chlorine using tabs, OR
+ You can run CYA=120+, but then raise your FC to 15 ppm, by dosing bleach 1 or 2x per week. You can use a partially filled floater to maintain CYA levels.

1,000s of pools in your area are run that way by service companies who inject chlorine gas 1x per week.

If your filter pressure has not increased, you should not clean it.