... keeps the whole thing inside a single s/// operator.

The only thing I would say about this is that you're firing up the eval-uator behind the scenes, so
    s/^ ~ .* /@{[  ${^MATCH} =~ tr#_#+#r  ]}/xp;
is (I think; haven't tested it) exactly equivalent to
    s/^ ~ .* / ${^MATCH} =~ tr#_#+#r /xpe;
That's an awful lot of moving parts for what seems a fairly simple match and transformation. Getting back to Eily's first solution and in particular to tybalt89's solution, I don't see a problem with something like (also untested):

while (<FILEHANDLE>) {
    tr/_/+/ if m{ \A ~ }xms;
    do_something_with_fixed_up_line($_);
    }
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Simple, clear, one-step fixup, do whatever you want with the line thereafter.

Oh, and BTW: Please don't use # as a delimiter for regex expressions; I know we're talking TimToady here, but there's no need for perversity!