You were definitely right that a standard M2x3 screw has a head that seems a little too small.
It is just catching on the m.2 SSD and keeping it tight, but the screw holding the m.2 drive in that came from the factory, which in the service manual just states m2x3 definitely has a bigger head than the ones I got.
Got the callipers out on mine and the head is about 3.9mm diameter which looking on ebay/amazon is about all that seems available here in the UK.
Tried customer support, but they've said I'm best taking it up with the UK spares and upgrades team, but the only number available was a premium rate '0871' number so I haven't tried them yet for the sake of a screw that should be pennies.
I am really surprised that as these machines are meant to be user upgradable, that something as simple as a screw for the spare m.2 slot isn't either included, or given as an option when buying the laptop, particularly when them seem to be a bit of a pain to try and get hold of.