Do you mean gently push the drivers into the cabinet by hand?
I tried that, and all three feel the same, with the exception that the bottom driver (the one affected) gives the lightest tick when I push it in, as if it perhaps just exactly scrapes on something. I can't feel anything when I push it, but with my ear all the way into the driver I can just exactly hear that very light tick.
Do you think that could the cause of the rattling?
I'm wondering if the warranty will be void if I unscrew the driver.
Other than this I couldn't feel or hear anything at all.

Yeah, my distorting XTZ woofer behaved similarly, just the light "scraping" feeling at some point in travel. It can be the damaged coil, or just a stray speck of dust. I managed to fix mine just by wiping the coil (by gently pushing the cone of the uninstalled speaker from the inside).

As for the warranty, better to ask GoldenEar.

Difficult to diagnose with the recording but there is no doubt something going on. When you have a minute can you give a call and we'll work on figuring it out.

Thanks.

I called earlier today and spoke to Sandy on the phone. He asked me to send an e-mail to Mary, which I sent after we hung up (although from a different e-mail than the one I'm registered with here), and he asked me to tell Mary that he suggested that GoldenEar send me a new driver that I could then replace myself (I live in Spain, so ...).
So hopefully it will all work out, although it might take a while because of the Corona virus lockdown .

Great, thanks for the update.

Stay safe!

Have you tried tightening the spikes on the base of the speaker? I had a small rattle on my Triton References and it was due to the spikes being loose.