The first future steam-hauled train through Dover that I've come across is operated by the same organisation who ran yesterday's Flying Scotsman, namely https://www.steamdreams.co.uk/tours.php
As with yesterday's, the main tour is from London to Canterbury (West). The question then is, how to get the engine pointing back towards London whilst the punters enjoy the city. In the absence of turntables, you need a loop or triangle - enter the mini tour from Canterbury West via Minster and Dover to Ashford, whereupon the diesel at the back hauls the entire train backwards to Canterbury.
Anyway, the next such mini tour is on Thursday 11th August. Precise timings for every rail-identified place are usually released very late on because photographers have a habit of doing daft things to get their shot, but a good site to check exactly where the train is (ie. how much longer you're going to be freezing your bits off - 74 minutes in my case) is the "detailed" option within https://www.realtimetrains.co.uk/