Gates at Miami are pretty much guaranteed to change. I wouldn't attempt cutting through the parking garages, especially if you haven't been to Miami before, just walk around the terminal. There are moving walkways up on the third level accessibly by elevator, but again, if you aren't already familiar, just plan to walk. As mentioned the Global Entry office is in the pre-security area, so you will only have to get back through security into Terminal E/D. If you have TSA pre I would walk back to D to use that, otherwise the E access is usually slow and you can use the sky train to make it down to the far end if close on time.