Most of them have specialty’s that they are really good and competitive at.I’m unsure where you are in the process but normally I advise clients to go get 1 preapproval from a reputable lender.

But I also have some student loans (~38k) and a car loan (~19k).

If you need to push a less critical date 1-2 days and you still have contingencies in place normally an email will suffice, assuming all party’s are cooperative. 

If you would normally pay $1000 for rent and with the house hack you still pay $500, you are still saving $6k/year.

A couple things to consider would be to possibly move car debt, personal loans or cc debt over to your husband (assuming you aren't joint) to loosen up your DTI.  

It's a popular loan style overseas that allows all normal banking deposits/idle funds to sit on your remaining balance and thus save interest cost.

Sometimes I come across doctors or lawyers looking to invest, but these people are normally working with real estate agents. 

The last hurdle was getting approved for a mortgage which normally would not have been a problem.

Is this even close to normal?

Says a lot about the poverty wages they normally are paid.About the only "saving grace" - if there is any - is the additional supplement for children / dependents.