You can find more information here for Houston Housing: https://housingforhouston.com/And  here for Harris County Housing Authority: https://hchatexas.org/

Would I need to build more tangible equity in the property to make it more advantageous for lenders to authorize a refinance/ secondary loan?

This is the firm founded by author Clint Coons who wrote Asset Protection for Real Estate Investors.I'd like to hear about your experiences, good or bad.  

They may not be authorized to do dual agency, or they may not feel it is in the best interest of their seller client if a listing is hot since dual agency can get messy. 

Go to their caseworker (if you don't know who it is, look up the local office of '(city/county) Housing Authority' and call the office.

Power of attorney is not permitted, but I did have one lender who blessed off on a corporate resolution for a stateside entity member to have signing authority for the business.

Once you start negotiating with a tenant, all of your authority and credibility goes out the window. 

Barbara Corcoran — How She Turned $1,000 into a $5B+ Empire: PR Stunts, Sales Techniques, Critical Early Wins, Fighting Trump, and Becoming a Real Estate Mogul (#725) - The Blog of Author Tim Ferriss

You have refused to sign this form along with your ACH authorization form & W9 form. 

Definitely get with their broker and if you don't get satisfaction there, contact the state regulation authority for real estate licensing to file a complaint.