You can try DoH to see if it is working.
It's port 443 so it won't get redirected by their filters.
Android uses DoT so maybe that works. Assuming that they don't block port 853.
Try the encrypted DNS option to see if they are blocking all DNS providers or just certain ones.
You can also setup your own encrypted DNS on a VPS if you're feeling brave.
I use enterprise drives because they're cheaper and more reliable.
Got some 4TB enterprise NVMe for 150 each. They only had 3TB written, basically brand new.