Result is that we have a little (oval - perhaps 80cm ?) sat dish up on
the gable end - with a clear view of the sky....

You need a bigger dish, probably round, not the little ovals you can use in
SE England.

The aerial is a 4 dipole + reflector arrangement, that they've
fitted in the loft (where it has to look through two concrete
walls and is about 1ft from an enormous steel 'I-beam' which
forms the ridge of the house. To compensate for this,
they've added a high-gain amplifier....

Ditch the amplifier. Waste of time. Amplifiers compensate for long downleads
or splitting. They are no good for rescuing below par aerial installations.

You have ghosting. There could be two causes of this. Firstly, your noisy
loft installation. Secondly, being close to a high power transmitter. I
can't say which problem you have.

The first will be fixed by installing outside. The second would be fixed by
using a log periodic aerial instead of a Yagi. Log periodics have lowish
gain (but do you care?) but, more importantly, are very good at eliminating
reflections without all the spurious peaks you get on a Yagi response chart.
You basically point at the transmitter and get a good signal.

If you have a really stubborn fixed reflection, such as off a large building
or mountain, you might need something more exotic, such as a Yagi phased
array, although these can be very problematic to set up (particularly
wideband) and are very sensitive to slippage from being blown around.

Christian.