I noticed that your sample $s is a non-matching one.
Did you take that on purpose to emphasise on cutting off backtracking in the failing case?
When I balance the (double)quotes in $s by adding one in last position (directly before the closing parentheses of q,) "straight" seems to have a slight edge over "cut"
Rate cut straight
cut 110876/s -- -13%
straight 127147/s 15% --
I got similar figures as you for your original $s
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