If you are checking in on a Saturday you may be in luck.
When we were there last month the CM at the front desk told us that with Saturday night points being so high relative to other nights, they often have rooms ready and cleaned very early on Saturdays in the off season (because people have checked out by Friday and the rooms sit empty Friday night).
This may only apply to 2 bedrooms because there are so many of them --not sure about a GV.
You may want to call the front desk a day or 2 before and tell them what you are thinking of--they might be able to tell you if a GV will be ready for early checkin.
Have fun--a GV at HH--sounds awesome!!