Even with low credit scores, you should get financing approved from Kubota credit, if you put a 30% down payment. That down payment shows you the buyer is making serious commitment, and financing companies can overrule your low credit score. Failure to achieve higher down payments at your income level, suggest hidden debt to financing companies. A $5k downpayment with $165k income suggests a problem of hidden debt, that's how they will see it.
The number of credit cards don't decrease credit scores, in fact more the better, if they are properly managed.
I will also say, don't apply to 2 or 3 tractor financing companies, and get rejected by then all. Because your credit scores will drop about 5 points with each official credit rejection.
Work with the dealer/manager and his credit department, informally and off the record, discussing various scenarios of down payments and length of loan, without such financing effort ever showing up on your credit report. Maybe this is not the year to buy a new tractor, next year is.
You need to work on credit rebuilding by paying off each credit card fully each month, and keeping your credit charges to no more than 15% of your card credit limit.
It may take years to rebuild credit scores after defaults or a registered bankruptcy. And current income is only a small part of credit score calculation, which is why I read millionaires often have the lowest credit scores per income levels, due to excessive debt loads in their past history. And your wife's income will not show up on your credit score or improve it or affect it in anyway, because she is a separate individual for your credit score calculation.
Again, high down payments allow financing companies to overrule low credit scores and make the loan, based on current income stability.