I too have an '06 Ram Laramie Mega Cab, dual climate control.
I had the recirc door break, fall down onto the guide over the blower motor and block the air flow. I worked to fix that problem without removing the dash, even installing a stop on the box that holds that door so the actuator motor doesn't put excess force on the door when in the recirculation mode. The new box had a stop in both places, whereas the old box in the truck only had a stop for the axle in the fresh air mode. Biggest problem was working next to the Infinity amp also mounted beside that acutator.
Well, before I put the glove box back and the mini floor console back, I heard something flopping around below and behind the center bezel, and investigated. I found when I would turn the mode dial from defrost, stopping through all the settings to vents, that when I went to the floor only setting, a plastic cam connected to a rod would flop around on the rod loose and head over to the driver's side of center. I found where that cam was to go into the plastic heater box and engage another lever, but the retaining clips had broken on the cam and it wouldn't stay in the hole.
After more reading, consulting my Dodge Service Manual, and looking at the entire system, this cam belonged to the passenger side "Mode 2" door which is supposed to adjust how much air goes to the windshield from floor to defrost setting. The actuator motor pulled it out of the dash, and then proceeded to turn far enough to break the driver's side mode 2 door. I too tried to stop that linkage by holding on to it while turning the mode knob, but the actuator motor was too strong, and pulled that link right out of my hands. Hard to believe that those actuators are that strong.
Here's the crazy part: The actuator movement is controlled by the computer as to how far they move, from pulses of voltage supplied by the computer, and can be reversed when the computer reverses polarity to the motor. The total travel of these actuators can be set by the DRBIII scan tool. However, every twenty starts, the computer sends out a signal to make the actuator go all the way one way, and all the way the other, to relearn the max travel of the actuator. That over-torqueing of each door by the actuator every twenty times the engine starts will cause failure of the doors by twisting them apart! That is ludicrous to have that programmed into the computer to do that, unless you want to sell a $1K service every so often to repair the heater/AC....
And, you are correct, there's no way to get to those actuators much less the blend doors behind the front of the dash, without complete dash removal. So, that is what I am into, beginning yesterday, following the service manual instructions to remove the dash and work on the heater/AC box. I'll have to get into it and see what damage has been done by the errant actuator motors and computer....