So if I’m understanding what I’m reading on 1033’s - house has mortgage of $350k and insurance policy is for $750k- leaving proceeds of $400k.  

A settlement with an insurance carrier or a court decision and judgment where insurance proceeds are available.

If the business sale proceeds or K1 are considered passive income, can the strategy as described here with my wife (no W2 income) as the active manager of an out of state STR property, work to offset the business sale proceeds?

I let them know, yes proceed on T&M not to exceed the original number and do not do any work above that number.Week later contractor finds an issue and says "hey, we have another issue and we can take care of it for $500, As it stands I believe I am going to come in under my estimated total." - So we authorize the work.Contractor submits the quote yesterday for $8k and is threatening me about it. 

As long as the aggregate net purchases are at least as much as your net sale you'll still defer all tax.The other consideration is that you can allocate your net proceeds in any way you want on those multiple purchases. 

What about a portfolio mortgage with the lender keeping the proceeds in trust for your purchases? 

Any recommendations on how to proceed?

From everything that I have been able to find, HUD does not forgive or back down, my mortgage company so far appears to be unwilling to back off the price, I doubt the buyer is willing to come up on their offer and I feel I am faced with 3 options: 1) I let the sale proceed and end up with no money, owing money, and no where to go, 2) The buyer proceeds to sue for the property because I signed a commitment to sell, I will end up with no way to relocate my family and nowhere to go, or 3) the home goes to auction and again, no way to relocate and nowhere to go.

If there's clear evidence of tenant misuse or negligence, I would proceed with charging the tenant.

I'd love to get your suggestions on how to proceed.