Hi Tracy,
The strollers at Disney can absolutely accommodate larger/older children. In fact, you will regularly see kids who are easily approaching six or seven riding around in them after their legs have called for a time out! Your son should have no problem fitting comfortably inside a rental stroller. You can save a bit on the daily rental price if you purchase a "length of stay" rental. For more information on rentals, including current pricing, click
HERE.
I have two other options for you to consider as well. I have tall kids as well, and was able to purchase a "gently used" MacClaren umbrella stroller on eBay for less than half of the retail price. It has a huge canopy (a life saver on a warm, sunny day), a small "basket/net" underneath, and folds in a snap. It's also super light. (My model can accommodate kids up to 55 pounds, and neither of my tall kids' heads hit the canopy.) I've also seen a Graco umbrella stroller that's quite similar that can accommodate larger/older children. Buying a stroller will likely cost you about the same as renting one for the week, and you'll have in outside the parks, which might come in handy as well.
Finally, I had a good experience with Orlando Stroller Rentals (orlandostrollerrentals.com) Their City Mini model is like a "slim" jogger, which maneuvers easily, but is not as large as a typical jogger. The single stroller can accommodate a child up to 50 pounds. Current pricing is available on their website. Strollers will be delivered to bell services at your resort, and you can return the stroller there before checking out on your last day. Again, this option will allow you to have a stroller outside the parks.
Whichever set of wheels you opt for, have a great trip!
Tanya