I did some more scoping of the generator today with JulianF's help
In all of these cases, the generator is not connected to the house. The scope is running from the mains supply (not generator) and any loads mentioned are running from the generator
Here is the genuine mains waveform

Here is generator output with no load at all. Nothing like a sine wave at all and more like a mountain range.

Here is the generator output with a purely resistive load (2.2KW electric kettle) only and nothing else. I expected this to be the best waveform but it is really spikey and triangular

and here it is driving a large motor load (2.5HP compressor on load). Despite being inductive, this is the closest to a sine wave and is actually not a bad waveform at all
