The physio was happy with the strength progress I'd made. He has given me different exercises to continue to work the glute medius and assorted surrounding muscles.
The bikefit was really interesting. Lots of questions to start, then measuring/mobility checks, then lots of riding the jig, adjusting it, riding it, adjusting something else etc. We spent a fair bit of time on the shoes/insoles as might be expected. End result - new insoles, cleat wedge, new saddle, bars, stem. Changed saddle height (down a bit and forwards), and shortened reach with the bar/stem change. All these changes basically meant my pain went away, so while we tried a different crank length, it wasn't deemed necessary to spend the money - might be worth trying the 170mm cranks if I still have issues riding outside. The video was pretty clear about how my original position was sitting me too high, resulting in me leaning to my left and over-extending my right leg, so much of the initial saddle adjustment was about correcting that before anything else.
Oddly, while the pain had arrived after a bit of pedalling, and was gone after the saddle adjustments, it came on after about 20 minutes in the car going home. Gonna continue to do my physio exercises and try riding my bike with the new setup on the weekend.