There really isn't a two person per bag limit on the ship or at least if it is, it is far from enforced.
They do include two luggage tags per person in your docs. When we checked in during our WDW stay prior to the cruise, we were asked if we would need additional tags, we said yes and were handed a stack.
In addition I have read of folks on here who have arrived at the terminal with more than two bags per person and are happily supplied additional luggage tags.
I don't think they really care how many bags you bring on per person, they all have to go in your stateroom someplace. So I assume that if you wanted to live with a half dozen bags per person in your stateroom, they would let you check them.
So I wouldn't worry about checking the stroller, I would expect no problems.