He would have trouble when it came time to refinance into a more reasonable conventional loan. 

SO, I do not meet the work/income history requirements for an FHA or Conventional loan (to my knowledge).

You plugged in a way too low rate for a conventional long term loan and costs. 3.75 30 year with $2500 on a cash out 4 plex investment loan you need 2-3 points or more to buy down to that rate so add $2400 + to your $2500.

Conventional Loan.We had an offer before of 305,000 but fell thru because a ****** appraisal of 284,000 using comps from 8 months ago and wouldn’t consider the new comps . 

If you are okay waiting 25 days to lock in good long term financing on a conventional loan instead of paying points and high interest on HML, those 25 days are definitely going to save you money in the long run.

A conventional investment loan will be limited to 80% of appraised value, usually called "20% down" although if the sale price is below appraised value that gets you in with < 20%. 

I have a few options, got prequalified for conventional loans, loan to purchase STR in Mexico, I have a HELOC I can tap into and I can create a Self directed IRA and purchase something with that.

I’m out of VA loan money and this will be our first actual conventional loan experience and it’s because of this that we’re thinking of doing a less than ideal home that we can fix up over time while saving for another more acceptable home to raise two growing boys in.

Wait, improve your credit, and then buy with a conventional mortgage.

I don't need an appraisal to come up all 52k, but it would need to come up to a reasonable actual fair value for me and seller to strike a deal, otherwise the logical step would be to relist and grab a conventional offer for tens of thousands more.