In September 2019, I travelled behind (4)5428 and (6)1264, and saw 76079; all of these travelled the whole route and didn't come off their respective trains.
I understand that in most cases the NYMR will try to roster a Whitby loco to run the whole of a Pickering - Whitby - Pickering diagram, but sometimes if this isn't possible they may operate another steam engine between Pickering - Grosmont and then use the diesel to take over to Whitby & back.
Last time I was there, which I think was Autumn 2018, 76079 brought us up from Whitby to Grosmont on the last journey back from Whitby, and was then due to be replaced by (6)1264 at Grosmont as '79 needed to go for a quick check up (the one they have to do every so many miles of service).
1264 was supposed to have arrived at Grosmont before us, having hauled the last Pickering - Grosmont service of the day. However, it was delayed and arrived after our train, so couldn't run around (both lines being occupied by a train). In the end, we waited around 20 minutes and then '79 returned to finish the journey.
In fairness, having '79 on was a bonus anyway because I'm pretty sure that the 17.20 (or thereabouts) ex-Whitby was, at the time, diagrammed for the Class 25. I don't mind that, but having been hauled by the 25 on the way out, I was desperately hoping for a steam loco on the way back so definitely a happy customer! 76079 did seem to struggle on the uphill section between Whitby and Grosmont tho. We were basically at walking pace at one point - think we may even have stopped once or twice.