FLHurricane.com: TS Dolly's interaction with the Yucatan?

I'm looking at IR and Water Vapor and came up with a question about Dolly's future.

Normally storms weaken when they pass overland. However, normally storms have their convective regions and eye structure disrupted, thus why they weaken. Looking at Dolly, her main convective zone is in her NE quadrant with almost nothing in the SW quadrant, that which will pass overland. Also, per recon, there was no eye structure detected yet.

So, the question is: how much will Dolly be weakened if she manages to pass her core over the tip of the Yucatan, but keeps her main convection zone out to sea? Specifically, what kind of disruption would we expect to see, and how quickly could she recover from it once in the Gulf?

(hope this is the right forum; it's a current storm, but it's also a question)