Perhaps you could divide the text into two elements and slant them differently.

That will be ugly. The text in the middle should not be slanted. Three elements then? You'll still see a clear difference with the gradual change in slant it should have.

I expect there should be a simple way to change something rectangular into a trapezium (that's trapezoid for you americans)... I just can't find it.

select the text, do (menu)Path->convert object to path - and so loads of crazy stuff with it

That way I can change the shape of each character separately. Not what I'm looking for. What I AM looking for, I was expecting to find as a tab in object->transform.

Maybe a more clear ascii art illustration helps:

+------+
| door |
| mat  |
+------+

should become

   +----+
  / door \
 /  M A T \
+----------+

With of course the slant of each character matching the perspective, and uppercase meaning increased size rather than change to uppercase.