The refrain from many travelers is they want to pay less because reimbursement has fallen off but they don't want to share a bath.   

They set themselves up for big losses when they cycle ramps back down and stabilizes to decades old norms.Texas as you know has very high property taxes and for multifamily can eat you alive as tenants do not reimburse like with retail.I can tell you in the 3 to 4 million range for multifamily nationally there are just tons and tons of buyers.

It would seem obvious that the 2nd would eagerly pay off the foreclosing first, but I'm unclear on the mechanism to do this (aside from just sending the mortgage company a check), and wondering how they eventually get reimbursed?

The buyer already agreed to pay for it and will be reimbursed by the seller at closing. 

We begun work before then on October 2021 (time of sales agreement) and they are willing to stipulate to we can be reimbursed for those 5ish months.

You can contact the water company and often they will help open a claim and reimburse you for a leak.

Since we will be receiving reimbursement checks, I want to take advantage of benefits offered from BUSINESS CREDIT CARDS.

I feel I should be entitled to those funds being reimbursed to me to put towards the new line since the neighbor is wanting out of the shared arrangement. 

If the buyer bought owner's title insurance, which we insist on, title will reimburse their loss.Original OwnerThe transaction gets reversed, and the original owner gets their property back, hopefully undamaged.

In addition to that there was a possibility that the magistrate/judge could possibly award damages to the tenant for defending against those provisions.So, instead of paying $600 (now property $1-2k) upfront for a good draft lease, total spend was $500 to be told the lease was bad, another $600 for a new lease, and lost $5-10k in damage reimbursement.