My DD's manual chair is a Quickie 2, so I have a picture in my mind now. I don't think you will have a problem getting it and the number of suitcases you are talking about into a towncar trunk. We have gotten DD's wheelchair (all taken apart) into a regular car trunk, but would not have had room for any suitcases. From what I have read, those towncar trunks are pretty large though. If you do go that route, I would take a bag to put the wheelchair tires in, so you don't have to worry about grease from tha axels.
We haven't used any of the towncar companies, so I don't have any idea of "attitude". There are several towncar companies besides Tiffany. And Mears wheelchair accessible van is the same price as a regular Mears transport. I lost my listing for it, but Mears also owns a taxi company (I think there is a link on Mears website) that has wheelchair accessible vans.
I would suggest looking around the Transportation Board for some of the other limo companies, then email the ones you find with your questions (it would help if you can "translate" the size of the wheelchair into a "suitcase" size. We did that a few years ago when we were thinking of not renting a van. We found Mears was the only one that emailed us back, so I guess the others were not really interested in passengers with wheelchairs.