I would also agree that you should bring your macs. I have travelled many, many times with my mac Quest over the past 3 years. I've always gate checked it without any type of travel bag and have never had it damaged by the baggage handlers. This includes several international flights, some with connections.
I have never been to WDW, but we have season passes to our local amusement park. We go all the time and have never had a problem with a stroller being stolen. We usually bring our Quest.
I can't imagine using one of the cheap umbrella strollers for such a big trip. I think you will miss all the conveniences of your macs.
DS - 10
DD - 8
Twin Girls - 6