Can you just call for a "van cab" or do you have to reserve it early? I contacted Mears but they seemed to only want to sell me a chartered vehicle and thats just too much money.
Alauniira, whenever my family has traveled to WDW as part of a group vacation, for those times when we needed to get somewhere quickly and didn't want to rely on Disney's transportation system, we asked Bell Services to call a van cab for us. It always worked out beautifully.
In your case, since you'll need more than one van and your event is very (very!) important, I would contact the cab company directly and let them know that I needed "x" number of van cabs to be at Pop Century at "y" time and on "z" date. I bet something could be arranged for you.
I'm not sure who has Disney's transportation contract for cabs this year, but if it is Mears and they are unwilling to work with you, then I would contact Yellow cab or another reputable cab company in the Orlando area. I would tell them what I needed and see what sort of transportation recommendation they could come up with.
Another option is to contact
FL Tours. They are one of the sponsors of the Dis website (
have been for six years). I have used them for my family's transportation needs between the airport & WDW, and I have always been pleased with their service. As a matter of fact, when I was recovering from leg surgery and was confined to a wheelchair, they actually sent a very nice van-type of vehicle to pick me up at the airport. Their driver couldn't have been nicer to me if she had tried.
Now that I've mentioned FL Tours, that is the route that I would take. Contact them and see what can be arranged for your budget & needs. Hopefully, they'll have a solution that will be perfect. But if they don't, then consider contacting a taxi cab company.
Good luck -- and, again, congratulations on your upcoming wedding!