If I do a relatively long East/West leg (yesterday was Biggin to Exeter, for example) if find that the line on SD is significantly displaced from that on the plumbed in GPSs (530/430/Pilot IIIc) to the extent that there is probably over a mile between them at the mid point. Thus, one can have a significant fly right on one and fly left on the other.

We could change the DI/HSI instrument to work with great circles instead of rhumb lines, in theory. But what is shown on the map would still be rhumb lines, and the PLOG would also be giving rhumb line headings to steer. This sounds like a potentially confusing state of affairs to me.