Would you consider taking a spare button and putting it in a mold made out of lego or something cheap and then selling packs of buttons in black plastic or rubber? They would keep the Dakota engraving without the white so would end up being accurate to the ones on screen that are basically plain black (I think they have some of the brown horn pattern but barely) and would be good to throw on any close shirt.
This would be the most ridiculous thing in pursuit of accuracy but it looks like the shirt matches the screen used one except for the puckering (not sure that’s the right term) at the seams.
That can happen because of thicker fabrics gathering during stitching, like with denim and the pictured tan shirt for example, or from heat shrinking due to washing since the stitches remain in place but the fabric itself gathers around them.
Would be interested to see how the black shirt looks after you’ve thrown it in the washer and dryer (the one in the show is distressed slightly even before Abby does anything so I think they would’ve cycled the shirts a few times) since that would confirm if the black shirt will end up looking like on screen or they really did dye a tan shirt, maybe they aimed for green but ended up with black.
Gee when I got into doctor who cosplay a decade and a half ago and discussions on dyeing trousers happened I didn’t think the details of heat shrinkage on cotton seams would stick so well, but here we are it turns out to be slightly helpful so much later ahah