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Many lender's have the option to pull alternate credit bureau's if needed. If applying for financing at the dealership and the lack of an auto loan on the credit bureau Ford Motor Credit is pulling becomes an issue, typically the Finance Manager can requeset FoMo Credit to pull an alternate bureau so the underwriter can see positive auto loan history.
Chances are high that going with a credit union wil get you the best rates when your scores are not elgible for special manufactuer rates. I suggest DCU or Penfed, probably DCU for your scores. If you can wait for a while and get your scores up I would do that because your scores are not great right now so some rebuilding would pay off nicely.