I was recently reminded of this thread so thought I should update it.
Six years later (six!) I have learnt a lot.
The Tsunami device I mentioned in my earlier posts turned out to be quite useless. I guess I was expecting too much.
A typical (affordable for a hobbyist!) digital scope is 8 bit or 12 bit, neither of which are much use for high resolution audiomeasurements.
I purchased a used Handyscope HS3
https://www.tiepie.com/en/usb-oscilloscope/handyscope-hs3 from 'TiePie' which has a 16 bit resolution mode with limited bandwidth (up to 200kHz from memory).
This has proven to be quite useful for tracking anomalies like oscillation etc.
But for measuring THD, SINAD and various other parameters, one really needs 24 bit, which means using a PC with sound card.
I purchased an Asus Xonar STX and using Wavespectra and Virtins Multi Instrument I am able to achieve some really useful measurements.
I created a dedicated page for audio test and measurement on my website for those interested.
https://gtkc.net/audio-test-and-measurement-for-diyI've attached a screenshot of a typical measurement.