Okay, this is going out on a limb, JPW, but humor me.
Three monitors on a laptop? Bear with me, but why? What is the scenario that will require three monitors?
Three separate students looking at information/videos/presentations, from the single laptop?
Two large monitors can do. THIS, is if we believe the foregoing information I am about to put out;
Not tested by me yet, but information has come to me that you can now attach a desktop graphics card, to a laptop.
A decent graphics card that is of the PCI Express 2.0 technology, and uses a PCI Express x16 expansion slot.
Granted the graphics card is an external unit, plus the expansion slot circuit board, and external desktop computer power supply, but you seem to have no problem with lugging around a docking station. (With port replicator capabilities)
I believe the above units can be placed in a single housing, with air cooling. (Fan/Fans)
Plus you will need a decent, reliable ATX power supply,
(Yes, I know the rebate ends at the end of this month, May 2012. It is just an example)
Two L-A-R-G-E monitors. How large? Have any 42 inch HDTV's around?
Just food for thought.