Nearly there:

$string =~ /$start(.+?)$end/s;
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The case insensitivity isn't needed in this case, but slurping everything up as one line is.

Then the match is stored in $1.

You don't need the quotemeta in this case (as Yves points out below), but I guess it's good practice to get into until you know *all* regex meta characters.

cLive ;-)