Appliance dolly for sure.
Strap that puppy in there. If it's a newer DMD era game you're gonna pout a blanket/pillow/cardboard between the head and the game when it's folded down. You should then wrap it with some plastic so it doen't come lose.
2 people is all you need. One lifted while the other person pushes from the bottom if going up or stops it from falling going down.
If you're moving EMs the head comes off and it's much easier/lighter. 3rd floor is a tuffy though. Besides your turning radius/landing you really need to pay attention to the floor material. If it's carpet you're good, if it's wood you gotta be careful.
If it's vinyl you have to make sure you don;t damage the floor when turning a 300lbs machine with all it's pressure on one wheel. I use some thin wood sheets you can buy at any hardware store
EDIT: Just gotta do it once to get the jist of it.