Thanks, everyone, for the great suggestions and advice! When we get closer to final payment, I'll reach out to Viking to ask about the Viking transfers (we are arriving the day of embarkation). I also like shipboy's suggestion of taking the Heathrow Express to Paddington and then a cab to the ship. In previous work trips to London, I've taken the Paddington-to-Heathrow Express which was quite easy to navigate even with luggage.