On 18 Oct, various folks helped me with my doormat and wrote:
...

Thanks guys.

The goat - disadvantages with the cat and the garden (and the goat
stand), but carbon-wise...

The £6.99 hair trimmers might be worth a go, so long as I'm not
tempted to try to save money on haircuts afterwards (those childhood
memories...)

Hedge trimmer - might need to wait until I'm alone in the house.
Orbital sander likewise.

Different thickness of doormat. Looks like the perfect solution.

Dig out the mat well/grind the well down. Good to see the UK D-I-Y
logical tool of Occam's angle grinder is applicable.

Thanks again

David