$s =~ y/*+!//d;

This would replace all the characters in $s, not only those in the end, and it would replace them in any sequence - so this is not useable in my situation.

No, it wouldn't (remove any character).
It removes any occurence of the characters '*', '+' and '!' (it's a use of the transliterate operator tr/// (same as y///). It doesn't care about the position of the characters.

$  perl -e 'my $s = "xyabcy*+!*+!*+!*+!*+!*+!"; $s =~ y/*+!//d; print 
+$s, $/;'
xyabcy
$  perl -e 'my $s = "*+!xyabcy*+!*+!*+!*+!*+!*+!"; $s =~ y/*+!//d; pri
+nt $s, $/;'
xyabcy
$
[download]

I don't think, that tr/// or y/// can help you with your chomp problem.

update: minor changes in text (... remove any char...)