Yes, the only way to get your CYA down is to exchange more water. This is really your only long term solution. I described above one way you can probably get your pool safe to swim in for the short term until you can drain more water. The good news is that one you get your CYA back in range, if you stick with TFP and follow the methods of pool care taught here, then this problem will never happen to your pool again.
I know that really sucks to hear, I was in a pretty similar spot when I found TFP. My CYA was probably in the 400 range and my pool was green. I was actually able to get my pool back to clear before my test kit showed up in the mail. I then found out how high my CYA was and tested my FC at I think 55! The FAS DPD chlorine test is only accurate to an FC of 50. I then had to let my FC drop to 0 to drain my pool to the street (city requirement where I live). I think that took a few weeks to drift down. So while this is not truely a TFP method, I think doing something similar in your pool would work in the short term to get your water safe until you can drain.
Another thing to note is that the pH test is not valid with FC levels over 10, so make sure to adjust your pH to 7.2 before bringing your FC over 10 since you won't be able to check pH again for a while.