I agree with the 'cheapy stroller' approach. I did this at WDW and DL. I bought an umbrella stroller for about $20 (including shipping) on EBay and had it sent to Florida, so it was there when we arrived. We left it with the Goodwill when we departed and even got a small tax writeoff for the charitable donation. Best of all, we didn't have to take the stroller on the plane.
For DL, we drove, and I was able to use one of the 'free' umbrella strollers they sometimes give away at Babies R Us with a large purchase.
Also, I have used the 'dirty diaper' trick, and so have many of my friends who took much more expensive strollers. You just take a diaper (not used) and pour some water in so it swells up, then smear some brown gunk (friend of mine used Hershey's syrup, I used BBQ sauce) at the leg openings... so that the diaper looks well used. Then put it in a clear plastic bag and tie it to the handle of your stroller. Trust me, NO ONE will want to touch that stroller!