you want st. andrews, and british rail stopped serving st. andrews in 1969: http://www.starlink-campaign.org.uk/
the closest station is leuchars 6 miles north; trains take only an hour from waverly, but then there is a bus ride or uber in to the city centre; so let's call that another 30 mins, and up the total waverly->st.andrews time to 90 minutes
in order to get the savings of staying in the same room that night you have to add that 90 minutes going back to edinburgh - you can get a car in downtown edinburgh the next day and drive to islay
but you lose the more efficient routing
drive to st. andrews, then drive to portree on skye - it's only 5 hours across the middle - do your skye time - then once a week macbrayne (this year it's on saturdays) runs oban to port askaig on the northeast side of islay itself - portree to port ellen is 8 hours of very hard driving - no motorways in scotland - 2 lanes the whole way - no passing - and probably 40 miles an hour the whole way - and that's nonstop - no meals - no bio breaks
note that the ferry schedules don't work the other direction - which means a 4 hour (not 2 hour) drive from oban to portree - but that doesn't matter because your going counter-clockwise to make the st. andrews day as efficient as possible
if you pair the frequent armadale-mallaig ferry with the once-a-week oban-port askaig ferry you have cut 8 hours of driving to 3, although the total door to door remains 8, you have turned the day in to part of the event, and you won't be driving through argyll twice, only once, and you can still get authentic 1000-year-old templar stuff in the middle of nowhere, and if the tides are right, splurge on the zodiac tour of the whirlpool
however, the whirlpool becomes a 2ndary consideration in your itinerary because the st.andrews-skye-islay triangle demotes the whirlpool tidal chart to 'is what it is'
note that you no longer need to drive to inverness to get out of scotland
but the flight situation is now different - glasgow or edinburgh to the US with a domestic switch to austin is a better play than coming home through heathrow - ***IF*** the flights can be figured out - because united and delta will probably have a better schedule/price for scotland->USswitch->austin than oneworld
note that lhr->aus is a noon departure, so either glasgow/edinburgh FLYING to LHR works - if you take a 430am train to kings cross
but more on flights later - still plenty of time to figure that out