Opportunity is missed by most people because it is dressed in overalls and looks like work. - Thomas Edison
if you have some puff additive you can use 2% or something around that as a DULLING paste. It won't puff up because there isn't much in it but it will take some of the gloss away.
I tried to get more specs about the sample from my contact. She doesn't have any idea how they were produced, not even sure they were produced in the states. This is a large retailer that has 6 colorways for this logo. They run about 4000 per month of each color. They sent me 3x3 sample pieces of the partial print and said to match. I don't have any problem matching the color, just the dull matte look. These samples are soft and very opaque. It looks like layered waterbase to me. If I go to a higher mesh the print isn't opaque enough on the Navy blend shirt. I will see if I have some puff around.