I think you might not recognize the difference between TC shudder and anything else that you think you do.
Your comment on #3 of "2nd gear and 1500 rpm doesn't yield enough torque - hence the drivetrain vibration" points this out to me - There is no possibility of torque converter lockup in 2nd gear, and you should be getting PLENTY of torque because 1500 is just below the torque peak for the engine. What MIGHT be happening is a reduction in fluid pressure, causing the converter to slip. If, as you suggest, you did not have enough torque to pull the load (and your converter was NOT slipping), the result would be that the load would pull the engine RPM down, and the engine would stall.
I'm probably the person on here that has pulled the heaviest loads with my CRD. I'm talking about a 60kW towable generator shown here:
http://www.cat.com/power-generation/rental-power/spec-sheets and click on the XQ60 for the full specs - Fully loaded, 6980 lbs. On that generator job, I also had to carry 500 feet of 1.25-inch diameter copper cables, which weigh in at about 2 lbs/foot or so, so I actually was towing almost 8000 lbs.
I have the GDE Eco-Tune, and the first TCM tune that Keith developed. This is not (as far as I am aware) anything special for towing. I DO NOT HAVE the "euro" converter, I have one that I bought from a transmission / engine shop that I trust. According to them, there isn't anything special about this converter, but it doesn't have any plastic parts in it at all.
Pulling that load, there is a bridge that I have to cross every day that is 1 mile long end-to-end, and rises about 280 feet above the water line. On one side of this, it starts only about 10 feet above the water. The other side, the approach is much shorter before entering the bridge, but you still have to make that climb. I don't know the actual grade, but I would suspect it is above 6% fairly easily.
My torque converter (or my driveline) do not shudder, vibrate, complain, break, stall, or anything else on this pull. It IS a tough pull, and I was only able to do it at about 55mph, and slowing down. I do not put my foot to the floor, but I do know that the EGT was pushing 1500 (pre-turbo) for that, and I was about 75% into the throttle. Going WOT just made the transmission drop into the next lower gear (2nd), skyrocket the RPM... And did exactly nothing for the speed or power of the pull - It only made a lot more engine noise and EGT.
1500 RPM is not too low to pull a grade, but it IS possible to out-power your torque converter still. What you think is driveline vibration... Where do you think that is coming from? Torque converter shudder when you are in a low-load situation, not towing anything... Would not be terribly violent feeling, because the output power is relatively low. When towing, ESPECIALLY when pulling a decent load (and I don't consider your trailer that heavy at all), the comparative POWER being output by the engine is much higher at EVERY SINGLE RPM level, so when the torque converter slips, why wouldn't that slippage be more violent?
You are experiencing torque converter slip, I'm sorry to say. Maybe an increase in line pressure would solve this for you. Maybe your dealer didn't actually put in the Euro converter. Maybe your valve body in the transmission has a tiny crack somewhere or one of the solenoids is leaking, and venting the pressure back to the pan. I don't know on any of that, but I do know that you can't have "driveline vibration under load" without having SOMETHING slipping somewhere. Every time it slips, it will try to catch itself - and slip again, and catch itself again... Causing a violent shuddering. The transmission itself is heavy gears. They don't slip, they break. If your CRD still moves - The gears aren't broken. Same for the transfer case. There isn't ANYTHING in the transfer case that allows slippage to the rear wheels. Same for the differential. Gears only. The ONLY PLACE that slip is allowed or could come from - the torque converter.