“The Rama says (and the Mishnah Berurah/Pri Megadim even say it’s ideal) to drink more than usual and fall asleep.”
Teenagers should not be drinking at all during the rest of the year except for wine at Kiddush and perhaps a drink on Simchas Torah. Therefore, drinking a small amount will be considered “more than usual” for them.
“it could be once an underage person drinks, he violates the secular law regardless of how much he drinks. So once he drinks more than usual, he has violated dina demalchusa dina, and drinking more won’t make the dina demalchusa dina worse. So once you have violated dina demalchusa dina to fulfill the main requirement, there might not be a reason (at least from the perspective of dina demalchusa dina) to stop there because you’re not violating any more secular laws.”
Incorrect. Secular law is more nuanced than you think it is. It’s not just a blanket restriction on underage drinking and that’s it. There are laws regarding providing alcohol to minors, public intoxication, etc. Furthermore, the more intoxicated a person gets, the more likely he is to suspend his common sense and do something that would be a violation of a different secular law. And of course, one should consider the fact that obviously intoxicated teenagers will attract more attention from police than those who have only had a little to drink and are functioning perfectly well.