I'm not sure if there is a better way, but to me the obvious approach is to accept 'start' followed by '(not start)*' followed by 'end':

my $lines = do { local $/; <DATA> };
$lines =~ s{
  ^ s \n                     # start line
  (?: ^ (?! s \n ) .* \n )*  # body excluding new start line
  ^ e\ p $                   # end line
}{}xmg;
print $lines;
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Note that this does more work than the original failing substitution, so you can expect it to be slower.

I'm assuming that the start of a test is "an 's' followed by a newline", and on that assumption being a bit stricter than your original example about matching that.

Hope this helps,

Hugo