Another month has flown by, so I suppose I ought to update.
I purchased the diff. mentioned before - reconditioned, no clunking backlash - and I had it fitted by the former Hobart Triumph dealership mechanic ... at a very reasonable price, too.
The good news: we needed the diff. - the old one was rather leaky and the oil was well dirty.
The bad news: some of the humming noise was in fact down to a worn rear hub bearing, diagnosed in seconds by the mechanic.
So, today the car is back in to have this changed ... it's going to be a pain if he can't reuse the UJ as the 'crossover' TriDat UJs aren't cheap - but then a bearing failure could be a bit messy to say the least!
Otherwise autumn is on its way here, and the car is getting a good regular soaking standing out on the driveway - it will be good to move to a place with a garage.