I've taken Uber to/from Melbourne and Vero Beach Resort. Worked really well. Sorry, have never hired a private car other than Uber so I can't attest to that.
I've used Quicksilver tours to drive me from MCO to WDW and would highly recommend them as well. They primarily offer service to/from WDW, but it may be worth a try to contact them and ask about Melbourne to Vero and see if they can do it.