Can anyone comment on anything that I'm doing wrong here? My skiing
on hard pistes has really improved but I'd like to get this area
resolved so that I can progress to steeper slopes with confidence.

Hire skiis or your own? (ie, shot edges)

It could be too that you have beginners skiis which are narrower and
softer in the tail. This will cause a tail skid unles you are very
light at the start of the turn.

Also, pushing into the front of the boot is an old technique fomr the
days of straight skiis, with carvers you weight the ski through the
balls of your feet.

Apart form that, make sure you get a good edge change (and good edge
angle by getting your knee well under your body)