We're there on Monday, too! We're locals, staying at the GCH for a short anniversary trip. (I'm an ex-Missouri girl, too.) Look for us - we DL DISers love to meet up to say hi at the parks. I'll have Lime Green Mickey Heads on both my brown diaper bag and dangling off our stroller handles and may make another one. We also have a Duo Quattro in Aqua and Brown (but may also use our Lime Green Quinny Buzz).
Which shuttle company are you using? That would tell me what your choice should be. If it's a smaller vehicle one like Super Shuttle, Road Runner, or one of those, I might feel better about it. If you are coming in from LAX, then the drive is longer. That combined with how some of those shuttle guys drive around here - I'd take the seat. (I used to commute to LAX weekly for business travel and had to switch to using a town car because I would always get nauseous from the shuttle drivers.)
If you were doing the big Gray Line DL Express bus, you don't need the seat at all. Kind of up to you.