My insurance agent often does an adequate job.That sentance alone tells me I should shop around agents/providers, but what is the easiest/most effective way to do that?

@Carlos C. in our opinion, the only real reason to put your properties in an LLC is for anonymity.Many investors screw this up though, by using their own name and address as the LLC Registered Agent:(All risk can be mitigated with enough insurance. 

There are several turnkey providers in town or investor friendly agents like myself.

I have agents who have sellers who have never seen a vacancy while they have owned.

Did you work with any real estate professionals (agents, lenders, etc.) that you'd recommend to others?

Your PMC is recommending the path of least resistance, because mold claims could be VERY expensive.Also, many insurance companies will NOT cover mold issues.So, call your insurance agent and see if this will be covered or not.At the same time, direct your PMC to get a professional mold test done to determine if there actually is a problem or the tenant is mistaken or exaggerating. 

Any references for a real estate agent in Texas? 

You should be 100% fine as long as you do the proper research into your agents, pm's, etc...

Sellers want to be on the MLS that covers the area where their home is located, so they can offer a commission to LOCAL buyer agents.2.

In the State of Washington, the buyer is entitled to possession of the home on the 20th day after the foreclosure sale.