The property says it doesn't have a shuttle, so why take the word of a taxi dispatcher? Or, at least call and ask before running back and forth.

Many airports will give a taxi driver a card which gets him to the head of the waiting line on return when he's taking a short hop. Some drivers have to wait 1+ hours for a fare so you can understand why taking a short ride becomes an economic hit.

You can remedy this by simply offering what seems to be fair for his wait.