As others said, this is a very labor intensive job just to remove the old stuff and is where you will spend the majority of your budget. Applying the new stuff once everything is prepped is much easier. A mobile tech is probably charging between $50 to $100+ an hour I would suspect. Before you call that guy, find someone and pay them $25 an hour to remove the old caulking. You only need the experienced guy for the re-application part.
Finally, I highly recommend getting the carport regardless. The thing that does the damage is the sun and keeping the camper covered will extend the life of the new caulk for many more years.