Thanks! I think that trick to pre-seat the tyre might be it.
@mdcc_tester I think at least part of the problem is the tyre bead just floating around above the central rim well to start with, nowhere near the bead seat, so there is more like a 5mm gap.
If it is genuinely a 5mm gap then it's never going to stay on the rim, let alone inflate. Unless you have some deeply weird rims with some obscurely cavernous central rim well.
https://www.youtube.com/watch?v=tE3h4nmDdOo
Have you tried this? Did the trick for me, no faffing with tape.