GTTTCTCCCATCTCTCCATCGGCATAAAAATACAGAATGATC
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which, while it is not correct, is not unspecified.

Well, I understand your point, but is it really incorrect? After all this sequence is preceded by ATG and followed by TAA, so it is in a certain way correct. But it is clearly not the smallest sequence matching this criteria in the input string.

This to say that, while:

  DB<2> print "$1\n"  while ($seq =~ m/(ATG(?:.*?)(TAG|TAA|TGA))/g);
ATGGTTTCTCCCATCTCTCCATCGGCATAA
ATGATCTAA
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seems to probably give a better answer, it is not completely clear whether the

(ATG)GTTTCTCCCATCTCTCCATCGGCATAAAAATACAGAATGATC(TAA)
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is a valid sequence or not.