Think morning as in for or nor
Mourning as in more sore/soar four
I know what you're getting at, but for my Estuary English accent all those words are the same
mafketis, r-colouring and rhotically trilling an r aren't quite the same thing. The word
nurse for example could have a delightfully rolled r inside it (which is how I now imagine Teffle talks) which is distinct from both its North American and RP pronunciation.
I don't have a problem with r, and I use it in a linking capacity regularly, but if it's making life hard for my students (np.
February) I'll tell them to ignore it, and just say
Febry. And if they're not colouring their r, but trilling it (as Poles are wont to do), then I'll remove the trill but not teach r-colouring, so "four" goes from "foo-errrr" (Polish) to "faw" (Standard English).