Now youāre speaking my language. This I can help with. 
First thingās first: if youāre not already using FSRS, you want to start using FSRS like yesterday. The best time is yesterday, the next best time is right now
If you are using FSRS, great weāll move on. If youāre not, let me know and weāll get you started
For backlogs there are three basic principles:
- Try to slow down the rate of adding new cards (if you can).
- If you are using FSRS we can adjust desired retention and/or reschedule some cards.
- Try to chip away at the backlog systematically.
There are two ways to chip away at a backlog:
- Set those cards into a separate subdeck and sort of chip away as you can.
- Set those cards, by priority, into filtered decks (which it sounds like youāre aware of), and snipe at particular high-priority targets first.
With backlogs there isnāt a 100% ābestā route. Personally, I like chopping them into more manageable chunks because it gives me little āvictoriesā and this is helpful psychologically. But really, the ābestā way is whatever way is sustainable and manageable for you that slowly, but surely, lets you play catch-up. Many ways to skin a cat, etc.
Personally, I donāt tend to use filtered decks very often. There is no good reason you canāt, but I find it more fuss than I need. I tend to organize by subdecks for the most part (in part because I donāt like having to ārebuildā the filtered decks each day).
Exactly right. So with filtered decks, theyāre really only designed to be used in short-term, super-targeted scenarios like sniping, specific review before an exam, etc.
About the only time I use them is like the day or two before an exam, when I know I need to look over, whatever, enzyme mechanics or something. Other than that I stick to decks/subdecks 99% of the time.
But, to answer your question: once you review a card in a filtered deck it just gets tucked back into the home deck from which it derived originally. You can ārebuildā it the next day and it will re-form the filtered deck based on whatever criteria you gave it. They are both handy, and annoying, for these reasons
I am sorry to report that, if you have this turned off, then the filtered decks are not chipping away at your backlog. 
You very much do want it to reschedule cards based on your answer in this deck.
Instead, in this case itās just acting like a little review session like, I donāt know, Quizlet or something.
TL; DR: If you have a backlog you 100% want to check āreschedule cards based on answers in this deckā checked ON. Otherwise youāre just doing free reviews for nothing. 
I donāt want this to get too long to let me know which questions you have and Iāll do my best to pile on.
Anki-nerd that I am, I also happen to be the lead maintainer for the MCAT deck and credit AnkiHub largely with getting me into medical school, so happy to help in whatever way/s that I can. 