This would have utterly nothing to do with whether or not your Beyer's are "beefy". It is a routing misunderstanding at the board. It would be foolish to get a headphone amplifier (at least for this scenario).
Go through the channel strips and at the bottom of each fader make sure the solo buttons are all in the off position. Not depressed. Go to the output section and above the headphone pots there is an Aux 1 AFL button and an Aux 2 AfL button. Those two should also be off (in the up position). Up further (physically_ on the board and to the left of the main information screen there are two pin-led warning lights. One is labeled USB and the other is labeled PFL/AFL. That is a quick eye-check warning that there is a PFL button (or AFL) left on. In most cases leaving a PFL depressed causes some degree of havoc and those small warning lights provide a quick reminder of what is currently set in the current configuration
This configuration changes the overall intent of what role the headphones play on the Model 12.
The Model 12, 16 and 24 are brilliant pieces of gear. I'd say my 16 and 24 are the single best investment in recording I've ever purchased. they are deep, deep feature set devices and it's impossible, virtually impossible, to run these things, even on a fundament level, without a very comprehensive understanding of the unit itself.
Without honestly reading the manual there'll undoubtedly be a hundred other small (or large) problems arise and they'll arise often.
You really have two devices here. One is a mixer. One is the interface. both at times happily share a particular setup and play nicely, the other scenarios may require a tweak in the mixer section or interface section.
To get the most out of this device you've gotta have a firm grasp of the manual. Otherwise, I can almost guarantee you'll be doomed to flounder.
Read the manual. You'll learn a bunch.