Neville,
I think that you have hit the nail on the head by looking at the calculations from first principles - I have never needed to calculate the pressure differential required to drive the thermosyphon effect before. It is a bit of an iterative process, but with water at 60 degrees C ( for the density) and a required ( my estimate) velocity of 0.5m/second the pressure differential to drive the flow 1meter is:
22mm inside diameter 1.00 inch head
28mm inside diameter 0.15 inch head
Thereafter for a 7m coil multiply the above differential by 7.
If you reduce the required velocity to 0.25m/second the equivalent pressure differential needed drops by a factor of 4.
At 0.125m/second the differential pressure required drops by a factor of 16.
There are rough estimates in the above for the friction factors and Reynolds Number. However, I was surprised by the significant influence that internal diameter has, and presumably in the longer term corrosion and silting of the flow pipework.