As a general update -- I did not call Heartland back yesterday, but did talk with Dicor. Apparently my roof is a Diflex ii TPO roof. I thought it was EPDM.
Long and short, Dicor pretty much told me that they did not see this as a roof warranty issue, but rather an install or an insurance issue. As they said it "the rook didn't fail, the installation failed." For the most part, I tend to agree with that.
They did spend a lot of time on the phone with me discussing my emergency fix. The one piece that I didn't really have calculated was how to splice the two pieces of roof together, and Dicor does make a specific Splicing Adhesive, which is on its way. So, I kind of feel good that there is an actual product designed to do what I need, which means my idea isn't completely crazy.
So, I have some TPO roofing material, some splicing adhesive and some water based roof to substrate adhesive all on the way to me now.
I still need to get up and take pics for either warranty or insurance purposes. It was just way to hot yesterday.