While Raleigh-Durham NC isn’t my part of NC I still figured I’d do a little looking online for you. So just letting you know, I’m not personally affiliated with these companies, nor have I personally used them. Anyway, I think I may of found two that could work for you:
I believe they primarily serve locals, but it looks like you can get a quote for any trip. You’ll definitely have to contact them to reserve any trip ahead of time.
They primarily do larger buses, but they do state that they have smaller transports for private trips. You’ll definitely have to contact them to reserve any trip ahead of time.
I would recommend discussing your needs in detail with them to make sure they will work with your trip, transportation time, and hopefully within your budget too. I also recommend asking them if they know any other taxi services that may have vans if they can’t meet your needs. It seems taxi companies in that area either don’t have wheelchair accessible vans or just don’t advertise they have them, hopefully one of these two will know who has some available.
I hope that helps,