If you're looking to move just from resort-to-resort, the Minnie Vans (via Lyft app) hold 6, have car seat options if needed, and are actually driven by CMs. It's $25 for one ride, so it may be slightly more pricey, but I'd give it a try if it looks like a good option for you!
Additionally, I found Lyft prices (rides, not Minnie Vans) to be slightly cheaper than Uber while on-site, and about $5-7 cheaper from MCO to WDW.
You would need an Uber XL or Lyft Plus for a party of that size, which there are obviously fewer of than sedans etc. but there should still be plenty of availability. I'd use both apps as sometimes availability or pricing is better on one compared to the other.