The only problem with that advise is there are no exits to the FL turnpike on SR417.
Your best bet is most likely Western Way to SR429. Go north on SR429 to the FL Turnpike and then you can go south. It's a lot longer than I4 to the turnpike, but will be less traffic.
Western Way starts at Buena Vista Dr at the Coronado Springs resort and goes right to SR429.
The other way is I4 north to the FL turnpike. Coming back to the Swan, take I4 south to SR536 and then get off at Buena Vista Blvd. You can also do the SR429 to Western Way to Buena Vista Blvd returning to the Swan also.