Note that in this case only your inner loop is doing any noticeable work (the printing), so you can just get rid of the outer loop.

while ( <RULE> ) {
  if (/^STMT/.../^STMT/) {
    print unless /^STMT/;
  }
}
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...or if you are into the whole brevity thang:

/^STMT/.../^STMT/ and !/^STMT/ and print while <RULE>;
__END__
A
B
C
Y
Z
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I used the ... operator instead of .. so that I could get away with the same pattern for both the left and the right sides of the operator, but I could have also used:

  if (/^STMT\d+=BEGIN/../^STMT\d+=END/)
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