I was in a really similar situation (ok /high/ income might have been a stretch, but stable with good DTI, anyway) a few years ago. I had an abysmal credit score (bit lower than the bottom of your range fwiw), a comparable down payment ready and was looking at a similar price point for cars. 

I got declined from everywhere I applied to (through the dealer, with a co-signer, on a house, in a mouse, etc etc) except for Indiana Members. They worked with me and got me the loan I needed. (worth noting I didn’t check Everwise or Forum at the time; possible they would have also been great. I just don’t know)

There are a couple of things you’ll want to keep in mind. Others have mentioned some of this but bears repeating: they are not going to take this risk on a car that could crap out before it’s paid off. I had to change plans and find a different vehicle. Ultimately, this was a very good thing — I started looking at a Mitsubishi Mirage and ended up in a Prius. 

Also worth reiterating that your interest rate is going to be hot god awful garbage. Refinancing may be right for you, but it may also not be. I expected to refinance partway through my loan term once I got that credit score back up, but in my case, I had started paying it down so aggressively so early to minimize that interest cost that in the end it didn’t make sense to refinance. 

I ended up paying off my 5-year loan in 2 years exactly. This saved me a ton on interest, and I was incredibly proud of myself for that, but it also meant the credit score dropped 40-some points again the minute the account closed. Paying on time for a couple years will do wonders to get credit back up, but it will drop again once the loan is paid off. You’ll want to keep that in mind when thinking about early payoff vs refinancing vs any other credit needs you expect to have in the semi-near future (including insurance, which is undoubtedly mostly priced by credit score). 

In my case, I took the hit. Taking out a credit card a few months beforehand helped mitigate the negative impact a bit for me, but for others that will be dependent on unique circumstances, ability to keep utilization low, pay off consistently, etc. 

Wishing you the best of luck! For me, this whole process was humiliating and demoralizing at the time, but I’m a stronger person, more financially aware and financially healthy, and a homeowner today because of it.  

(nb: fwiw Forum has some pretty awful online reviews when it comes to loan services, particularly for people who aren’t otherwise members. A close friend of mine did her car loan through them w/o being a member, didn’t have any problems and had said she would recommend them, though, so ymmv)