Don't worry about your looks, on a good day I look worse!
A few years back we tried dealing with a breed specific rescue, it was the same thing. Lengthy forms, references who were contacted, phone interview, and home inspection. Never mind we had the same breed, a Cairn terrier, for nearly 16 years before hand, or that we've had other small terriers for many years before that. OK, we can go through all that.
We passed, no problem, actually too good. The woman who did the home inspection was so pushing us to be a foster home for rescues. I would love to, if we had that sort of time, but we were looking for a family pet to live here the rest of their life. I know myself, and my family, if we had the time to foster rescues few if any would leave. Just like this woman wouldn't leave, and kept showing up, and calling, and showing up...
While I do respect the precautions they go through, we didn't need to be pushed into a situation that were were in no way ready to handle. While I rarely push what I do with fish on people, this one got it after too much pushy intrusion, I tried sending her home with tanks, not just one. It put the whole family off to this organization.
So, you don't want to do too good, they may want to turn your home into an animal care facility. Leave a few things for them to find that need to be corrected, not big things, just enough for them to comment on.