Hello!
Original poster here, and I'm just following up.
I did get a message back from the customer service department of the company (5.11) that made the two tactical polo shirts in question. They advise that the shirts, though 100% cotton, have been treated with a special "anti-fade" coating that would inhibit the dye from taking. That's it: closure on this issue.
It's more than a little bit ironic that these two new-with-tags shirts will now be relegated to the trash bin because their original color has been compromised around the collar due to sun exposure on display mannequins, and though they are 100% cotton, the "anti-fade" treatment applied by the manufacturer precludes my attempts at restoring the color through dyeing.