If that is the case, does the executor of the will, in this case his sister have any influence on whom the trustees sell the house too?

@Jacob Zivanovich other than an ego boost, NOTHING GOOD COMES FROM TENANTS KNOWING YOU ARE THE OWNER!

Then you  have out of state buyers that simply do not know what they do not know.. they tend to be influenced by on line reports of what one should make on a property IE it MUST Cash flow day one with minimum down.

Was the grantor competent to sign the deed or does the fact that she was 98 years old and in a nursing home when the evil sister (ES) had her sign the deed that left out her other daughter and son render her subject to claims of incompetency to the undue influence of ES? 

One more option that will reduce monthly expenses, and boost your rent a bit too is to buy a new home.

Customizable Adventures: We can tailor the payment plan to fit your lifestyle like a glove, offering flexibility that’s as refreshing as a summer breeze.Tax-Savvy Moves: Spread out the sale and dance around those hefty capital gains taxes, keeping more money in your pocket.A Legacy of Ease: Rather than a sudden windfall, seller financing allows you to sprinkle your wealth to your heirs, ensuring their financial serenity.Smooth Sailing: Forget the banks and their mountains of paperwork; our path is paved with minimal hassle and maximum ease.A Sure Thing: Opening the door to seller financing means more interested buyers might come knocking, boosting the chances of a sale that makes everyone happy.Convinced?

I would make sure you read Mark Simpson (Boostly) books.

You only get so much time boosted as new, so no need to waste it when it's not ready.  

Signing up for something like Experian Boost can help raise your credit score.

You'd just have to ask if these influence the carriers premium, and by how much to see if they're even worth consideration.