What happens when she clears the shear, on the opposite side of the peninsula? Does that open up a more northerly track?
At some point she will bump into the ridge and the track will start to flatten out to the west, for a time at least. The question after that becomes the western weakness in the ridge (where it doesn't fully connect to the Rockies ridge). We also have a shortwave trough coming into the NW U.S. right now, that could aid in bumping her north for a time before landfall. Currently, the weakness is enough to allow her to glide into S. TX, but most models have forecasted it to fill in... the trend today was north, still waiting on some of tonights models.
Shear should be relatively light in the GOM, and there is a large area of 30C+ water she will have to cross on her way into N Mexico/S Texas. Depending on how much she weakens crossing the Yucatan, I would think she could get back to cat 4 again at some point in the GOM.