First I would have a non-dealer electric specialist confirm it is actually the starter.
I had the same problem with a high mileage 2004 Pilot. Local dealer told me it was starter (expensive). I towed it to my independent shop for a second opinion. They kept it a couple of days and tested it multiple times and they found a corroded/worn main relay. Which is a $50 part!
Original Starter continued to function fine with new relay.