@bostonphil- a HEX ticket is only available on the day it is issued for whether an advance or a full price fare.
Elizabeth Line you just buy on the day.
There are no guarantees but unless there is massive service disruption you will get a seat on either service joining at Heathrow.
I am assuming you are staying on Bayswater Road (rather than Bayside),
If you changed off the Elizabeth Line at Ealing Broadway onto the Central line that would take you to Queensway and to Lancaster Gate stations- they are on Bayswater Road so may be closer to your hotel.
If you go Nat Ex I would take bus #148 to Victoria Station then walk down Buckingham Palace Road to the Coach Station. You 'should' be able to turn up and go on the coach but it is always better to book ahead, if only by a day or two.
If you take the train those leave from Waterloo Station. Take the bus #148 as above then anywhere between Victoria Station and Westminster change onto the #211 for Waterloo. The transfer is free so you only pay one fare.
You can pay on the day for the train, and it is very unlikely they would be full if travelling in the off peak as you would.
There is an hourly train from Victoria, but it takes twice as long as from Waterloo. On that route advance fares start from £6.
If you just turn up you will pay £41, if you book ahead you may get a fare as low as £9.20, more likely £14.50 or so.