Your DD period will allow you to verify some of that information, like cross checking the leases that you will now have access to with the rent roll provided to you prior to LOI submission.

The problem is that the way the property was renovated means that it does not allow for two couples and a shared kid (and maybe one more one day).

As long as the local law allows that mixture of tenants you cannot ask for more rent due to a large family.  

I'd be able to cover the loan payment based on what I'm typically offered for a housing allowance.

Check with your lender (and several others) to see if they have a seasoning period before allowing a cash out refi.

If you were to setup such a plan and start receiving returns from a property investment, you could reinvest that return into anything the IRS rules allow.  

I am currently in the process of getting a HELOC for 50% of the value which seems to be the max amount Texas laws allow for a single cash out loan (or so Ive been told!) 

His response was that yes, the T6-8/T5 etc allowances will be applicable even to a property under 5,000 SF.

Specifically, I'd like to know if there's a stated maximum allowable time limit?  

Seriously, I never get owners who allow their tenants to push them around to the point where they cannot access the unit.