I definitely wouldn't roll the wheels of the cabs across the laminate.
I've only moved a few cabs, but one trick I use for moving large objects on hard floors is to lay it down on an old comforter then drag the comforter.
Harbor Freight sells a "bigfoot" hand truck that is easier to get up and down stairs.
http://www.harborfreight.com/bigfoot-hand-truck-97568.html#pr-header-back-to-top-linkI helped a friend move a woodstove out of a basement with one and was impressed with it enough to buy one for myself.
Put air in the tires before moving anything heavy.
If it were me, I'd have a couple friends on hand, strap the cabs to the bigfoot handtruck one at a time, and make the trip all the way from outside to basement in one shot before unstrapping it.
Typically I'll run straps to the hand truck and lower it down from above.
EDIT: To elaborate, I'll hook both ends of a strap to the hand cart and then stand inside the loop with the strap going across my back. That way I can use my legs to hold the weight while lowering it down the stairs instead of trying to hold onto the cart hunched over.