Advice on credit situation/home loan?

Here is my situation, my husband and I really need to purchase a home. Earlier this year I checked my credit report because I knew there would be old accounts that needed mending. I pulled my score it was just under 600. I paid off everything in collections, consolidated my student loans. I just have student... show more Here is my situation, my husband and I really need to purchase a home.
Earlier this year I checked my credit report because I knew there would be old accounts that needed mending. I pulled my score it was just under 600. I paid off everything in collections, consolidated my student loans. I just have student loans, no other auto loan, credit card or any other open debt. My husband on the other hand has a handful of pretty old debt as well, stemming from his previous marriage. His score is at 545, mine got bumped up to 625 and its only been a couple months, some more updates should go through as well.
Anyways we currently have $10,000 in savings from an inheritance. We also are set to receive approximately $45,000 more in august.

I talked to the banker and he said with the credit scores so low there is nothing that can be done at this point. If we can get the credit score up by august, then the bank might possibly be able to offer an adjustable loan with 20% down. We can then refinance at a later date for fixed rate after our credit goes up some more. He did say that with lower scores there will be high fees associated with a loan. His other suggestion was just to work on the credit scores, and wait a year and then reapply for a loan, where we would qualify for 30 yr fixed with lower fees.

But we literally are desperate for a house we have 4 kids, I need to work from home as soon as I can and we have no space to do it. Our lease ends in august so we probably won’t get the rest of the inheritance by then to get an adjustable loan. We could probably work with our landlord on renting a shortened lease but it’s hard to know.

What do you think is the best thing we could do? 1)use some of the $10,000 to pay of my husbands old debt *in hopes* it will bring his credit score up enough to 620 (possibly open a credit card in his name in the mean time to help with that, 2) try to get his score up somewhat and go for the adjustable mortgage with the 20% down payment (looking at $140,000) house, or 3)wait another whole year to buy a house even though it will be pretty unbearable! but the interests rates will probably climb and id ont’ know how much I will actually save in fees by waiting a whole year if interests rates are climbing anyways.

Please your advice
Update: Thanks can you share some advice on negotiating the collections? they area ll very old, nearly 7 years! i was under the impression they fall off after 7 years and we are literally just about 7 years (in a couple months)
Update 2: thank you there are no judgements against him, just in collections. we make about $56,000 a year
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