I just got back and went to both EMH at HS and AK. It seems like I read a sign somewhere that said buses start 45 minutes before opening.
HS EMH was 6:00 am, we got on the bus around 5:40ish. We were there before 6am. No huge crowds. Little to no wait on about everything. We headed to Toystory first and rode all rides then headed to TOT and Rock n Roll then finally to the ride in Star Wars. We waited about 25 minutes to ride the Star Wars ride.
Our Ak morning was 7am for EMH. We hopped on around 6:45am. Again no big crowds at the gate but FOP was already at 60 minutes at 7am. We didn't ride it right away so I don't know how accurate the wait time really was. Navi was a walk on as was everything else.