Welcome!
You're sort of in the bind I was in when i took over my pool care. High CYA and water restrictions. Two things to do now: 1) Repeat the CYA test using the dilution instructions in
http://www.troublefreepool.com/threads/24188-Extended-Test-Kit-Directions post #8, step 9. 2) Get onto your water company website and see if you're having tiered water rates, mandatory reductions, or anything that says what to do about pool refills. Sometimes they'll let you change the water every few years and pay the lower tier rates. So do look.
If you can get way with a partial drain and refill, I'd say do it now while you still can. You can maintain a pool with high CYA; I've done it. I also know it's not something I want to do again, nor do I recommend it to anyone. If you can get away with dumping half, even a quarter of the pool water, do it. It's so much easier to maintain with the CYA at a reasonable level.
If a green lawn isn't a criminal offense yet, you can also use a submersible pump (or the hose bib if you have one on the plumbing) to use pool water on the lawn, then make it up with what you would have used on the lawn. That will sloooooowly lower CYA.
The ugly alternative is to maintain the right FC level for your super-high CYA, which could put it way up there into double digits. The CYA scale isn't equidistant graduations. What you guess is 110 could easily be 150 or 200. Hence the recommendation to repeat the test and get a number. If CYA is so high that you need to maintain double-digit FC, your pH test will always be somewhat suspect. The pH test is only 100% accurate if FC is below 10. The good news is that even if FC is at 15 or 20 - whatever
Pool Math calculates - you won't be bleaching out swimsuits.