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BeBop, Welcome to the Mortgage forum!
IMO, you and your partner would be better off repairing both of your credit files. You are well on your way and, not knowing what is on your partner's file, it is not impossible to repair his file. Go to the credit repair forum here with your partner. You might be surprised at how much you can get done rather quickly. The recent repo on your partners file is an issue. How recent is it? Can he contact the creditor and make a settlement? I am thinking something along the lines of a PFD (pay for delete).
In order to use your partner's income, both of your have to be on the mortgage and both of your credit scores are used. As pointed out before, the lower of the mid scores will be used.
Normally I recommend going to a CU for most credit related persuits. However, with a mortgage, you are probably better off going to a mortgage banker that funds their own loans and then sells them to one of the big mortgage companies after you close. They generally have a larger selection for your mortgage type and can handle exceptions a little more easily. I don't want to mislead you at all, the recent repo is definately an issue. It will need to be handled prior to your obtaining a mortgage if your partner is going to be on the loan.
If your partner's credit is such that he can't get on the loan, even after repair, then consider doing the loan yourself. In order to increase the amount you can borrow, you need to get rid of one of your long term loans. Probably the car as the balance is lower. Can you either sell the car or pay the loan off? Right now you have $537 in monthly debt and part of that is imipacting how much you can buy given your present income.