Aaaah, what a light bulb moment - thank you, Firefly258! I was a real blockhead not to see that as an anchor $ can only match a position between two characters or "between" a character and the beginning/end of a string, just as it is with the anchors \b and \B.

I must confess I'm still not very familiar with the qr// operator (but be assured that perlretut has been pushed onto my 2do stack ;-) so I tried

   my $regexp = 'some$' . "\nthing";
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and, finally, /$regexp/m matched "some\nthing".

Thanks again. You Monks are great!