High CYA

So....I've been following this forum for a year or two now and just realized that our fearless leader seems to be MIA. However, my registration was accepted so I figured wth...I'll give a try anyway. I've read so much at this point that I think I've confused my self. so here's my issue...opened the pool a few weeks ago, got it cleared up, including the algae but then couldn't keep my chlorine levels up.
My current readings are:
FC 12 (only because I dump a gallon or two of bleach in once or twice a day)
CC < 1
Ph 7.6
Alkalinity 110
CYA 120 (when diluted with tap water)
I'm using the Taylor K2006C, vinyl pool, in floor cleaning system, no heater, cartridge filter

From everything I'm reading I'm guessing it's due to the CYA level but is there any way to reduce it? This is where I've gotten confused...one of the posts recommended raising the FC to shock levels but I think that was in order to get rid of algae (which doesn't seem to be my problem). Is the only solutions to drain and refill or am I stuck just dumping bleach in continually?
For whoever may see this....thank you for keeping up this forum. The info is invaluable and I've learned so much already.
bwear