A property manager not requiring this raises serious red flags.

What are the density requirements?

LIHTC properties can have requirements that stay with the property for up to 15 years.

How do you think the 2 relatives will feel about having their rent raised or being required to pay rent period?

We only require a soft credit check as well. 

Title III of the ADA requires the removal of architectural barriers in existing facilities unless it can be shown that removing the barrier is "not readily achievable."

Known as an Improvement or Build-to-Suit Exchange, the process requires a Qualified Intermediary (QI) to hold the proceeds, and an Exchange Accommodation Titleholder (EAT) typically oversees the improvements.

Your payment requirement would rule you out for us. 

I have some of the required funds in a HYSA, but will most likely need to draw from another account and I'm curious which method is the most efficient in terms of taxes/capital gains, penalties, loan repayments, etc.Based on my previous transactions in the market, I estimate ~$45k cash to close: $20k for the down payment, $15k for closing costs and prepaids, and $10k of starting reserves.

Again, knowing nothing about this particular company, my bet is that type of company will require money up front just to consider whether they can help you out.