We have gate checked strollers and wheelchairs (for my mother) without difficulty for years on SW...now granted I never owned a stroller that cost more than my first car....I know a lot of people would never dream of gate checking their mega strollers...but it won't get any more beat up being gate checked than checked as luggage so I would rather have it in the airport for ease of travel as well as child containment in the gate area.
If your stroller is worth more than your next house payment I would suggest heading to
Walmart or Target and buying a couple of $20 umbrella strollers just for the trip....here's why.... if something happens to one of them...so what, no major investment (the airline will replace it for you without a hassle....my SIL got a check for one that got lost in the shuffle the night it disappeared)....also my kids loved to ride in them once they were walking good....better visibility than sitting behind your sibling in the double stroller, much easier in and out at rides, etc. in the parks....I never worried my way through a ride or show wondering if someone had swiped my cheapo stroller... and last but not least....folding up your humongo double stroller and lugging it and 2 small tikes onto and off of 1 WDW bus will make you wish you had taken my advice....1 quick kick and the umbrella is folded and over your arm and you still have a hand free to hold onto the kiddos.