When are you going? When we stayed at the Grand Floridian in early December there was never a problem, not even at park opening time. There were always a lot of people who got off at the Poly and the Grand for the breakfasts making room for those arriving
We've stayed at the GF in July, August and December and never have had a problem with the monorail even early in the morning. Once in a while DH would have to stand but the kids and I have always had a seat.
Standing up on that very, very short air-conditioned hop will be N-O-T-H-I-N-G compared to all the standing you are GOING to be doing, starting in about 6 minutes from that point.