After failing repeatedly to transfer my existing TM backup (on case sensitive drive) to a new, larger HD I gave up and decided to start again.
External WD Passport 2 TB drive - partitioned to Extended Journaled, this time case insensitive.
Speed test on the drive itsef connected via USB gave me write speed of 84MB/s. I'm not enough of a techie to understand how this might correlate to actual backup times. However, for 300GB (the amount of data I have to backup) and based on the speed test, a full backup should complete in ~1 hour.
I start Time Machine.... TWO DAYS it says.
Reading through this thread, I ran the TM Diagnostic via Terminal. Reformatted the drive and started again.
Initially read said 5 hours. Huge improvement over two days. After the first 10GB transferred (which took about 10 minutes) the estimate is now down to 4 hours; now 15 minutes in I seem to be at a consistent 1GB per minute transfer rate.
I have no idea what the benchmark for this tranfer should be but I can live with 4-5 hours a lot easier than two days. So, the TM Diagnostic is at least worth a try in my opinion.