My experience with a large propane company is not great and they seem to know every trick in the book.
I would suggest hooking up your old tank to the house temporarily and using the propane until it is empty and then switching. I'm a little surprised that your new company didn't offer to do that.
I would factor in what the time/mental hassle might be to get paid for "your" propane remaining in your old tank. After my experiences, if you can't do a temporary hook up, I would be inclined to write it off as the cost of having done business with the old company.
We are in the process of switching from propane because our experience was so unpleasant over something that could have been easily handled by the propane company and was entirely their fault. (Their tank leaked my propane, and they dragged their feet about both replacing the tank, and for (partially) reimbursing us for our lost propane. It took months, and in the end had interventions by attorney generals in more than one state. I think that it was the ugliest (on their part) interaction that I can recall with a business.)
So, yes, I don't have an especially high opinion of at least one propane company.
All the best,
Peter