This is not going well.
I ended up buying this. Mainly because I thought it was the right thing, but more that I could get it the next day (bless, Amazon, bless).
I have one bit of bad news and one bit of half bad news.
The bad news is that the connectors from the tool kit I got do not work with the allegedly Euro set purchased from Amazon.

The tool kit connectors are exemplified by the one on the tube. The kit connector is exemplified but the male connector at bottom left. They are quite different.
the picture below shows the innards of the Euro connector and the one on the compressor.

Quite different!
The half bad news is that the screw thread on euro connectors sort of matches the thread on the compressor. Sort of because it only screws in part way. Certainly less than the existing connectors. Which makes me think that the female thread is also tapered. And I'm not sure I can (Per a comment above) reliably use a non tapered male with a tapered female.
I'm stuck for what to do next. I don't know what the two mystery connectors are (the one on the tube and the one on the compressor connector). I've also struggled to find any male tapered connectors on Amazon (at least without paying a substantial price -and amazon includes BSP in searches for BSPT it would seem).
So. If anyone knows what the actual connector is on the compressor I can attempt to find a convertor. If anyone can recommend a supplier of BSPT connectors (at a reasonable price) I can replace the current connectors.
I'm still a bit stuck with what sort of tools to get. The ones I have already (as per the connector on the tube) or the Euro ones which Lidl/Aldi will provide cheap tooling for.
I really am stuck here, so any input would be appreciated.
Iain