Just wrapping up this thread. I ended up getting a second-hand Agilent 34401A. Spent about US$350 for a unit in pretty clean condition, good display, and as best I can tell, about 10-11 years old. It is out of calibration, but only just (was calibrated last year, due for re-cal in Jan 2017). Shipping to Aus was a bit of a hassle to organise, but ended up ok in the end.
To be honest, the Instek 8251 would have been sufficient for the work I had to do in the short term, and if money was very tight I would have bought one. But I'm happy that I've now got a unit which I can rely on for many years to come.
Thanks to all who posted their thoughts and suggestions. All very helpful.