They actually ripen really sweet like that. The main difference is that you get a little bit of tart to add complexity to what most would consider a one-dimensional mango (NDM) -- and you don't need to slurp down the slimy gel around the seed (that totally grosses me out :-).
If you pick too early, then yah, you get a sour mango with little sugar development. Timing is key -- and that takes a lot of trial and error. Must be picked "mature green."
The cogshall is notorious for developing jelly seed in this area. In some years, the majority of the crop ripens unevenly. So, you have little choice but to pull them green if you don't want to divert them to the trash can.
And then we have your favorite, the carrie, which turns into orange mango soup if not plucked green :-).
It's counter-intuitive, but many mango cultivars actually taste better if picked green and matured indoors. Nam doc mai, Carrie, and Cogshall are 3 that come to mind. Picking mature green precludes the jelly seed issue and causes the ripe fruit to retain a bit more acidity, which adds to the flavor. Most backyard growers are afraid to pick their mangoes green, because they think that the fruit only hits full flavor if left to ripen on the tree.
You should be able to pick your cogshalls with impunity by now (assuming you're in FL). Mine are all ready to be picked at this point.
Taste is subjective. ..to me, a NDM or Cogshall dont not ripen that sweet if picked green. I know you like that acidic component of a Cogshall when picked early and there is nothing wrong with that but to me, its not to my liking. If I am going to eat these varieties, I prefer the NDM with a yellow coloration and Cogshall with the haze over the color gone and an actual color break/turn.
Obviously for shipping, the "rules" are different. For best results, I recommend Fedex overnight when shipping fruit, whether its mzngoes, 'moyas or mandarins.