Thanks for the responses, people. The ideas about doormats and oak filler strips/ramps sound quite promising. While these door seals are certainly not structural elements and could be cut away, I think I'll leave the tools of mass construction in the shed for the time being.
There is more to this episode than I've told. The rest may come out later depending on whether the supplier honks me off more than they already have and/or I need to raise a mis-selling complaint against them for other, related, activities.
I think I'll pop out to the doormat shop at lunchtime ...