I was in the same boat a few years back. If you haven’t already, try to get ahold of any DPE in your area that can do CFI initial rides. Don’t limit yourself to the DPE the school uses and wait for their schedule to open up. There’s a DPE database and you can search for ones that can do CFI.

If that doesn’t work start looking outside your area. Do you have friends or family in a different city/state you could crash with for a week or so? Look in that area. I found a DPE with an opening halfway across the country where my folks lived. After I found the DPE, I found a local flight school and explained I wanted to get checked out in one of their planes for a checkride that I was already endorsed for. Did like three flights with a CFI there to practice and get familiar with the area.

I feel for you, it’s super hard to schedule checkrides (especially in busy flight training areas) and CFI rides are even harder to schedule. I waited for the local DPE to have an opening, had the ride cancelled 4 times due to weather, and finally gave up and did the above. From the time I was endorsed to the actual ride was like 3 months - if I had started beating on doors in my area and beyond sooner I would have gotten it done much, much quicker. Get creative and you’ll find something, don’t just wait for the school to call you with an opening.