You described your take-off shudder well. For openers, this is not likely converter related, as the converter clutch is not active at this speed. If it is the converter, this means the converter clutch is dragging, in which case the symptoms would get steadily worse and cook the converter. If you do suspect the converter, I can share how to test it in the truck.
Some would jump to transmission issues like band adjustment or worn clutch packs, motor mount issues, with the Cummins especially, and surely this could contribute. Likely you have done the band adjustment during service work, though. There would also be a benefit to upgrading to the aluminum accumulator piston that I describe and install in my Sonnax survival upgrades. See that article at: http://www.4wdmechan...nsmissions.html. You'll see the accumulator piston change there, too.
I like your gut comparison to the Ford Powerstroke that lost its clutch and flywheel harmonic dampening with the solid flywheel and clutch install. You may have a similar harmonic or actual binding issue with the shudder you describe. This may come as a surprise, but I would look elsewhere for that load shudder when you get the truck moving: check the rear driveline/U-joint angles. You have a 6-inch lift on the truck, and I'll share some pointers here.
Your Mega Cab wheelbase likely uses the two-piece driveshaft. If so, the shaft from the transfer case to mid-shaft bearing is probably stock still. Maybe you've dropped the mid-shaft bearing to reduce driveline angle at the rear piece. In any case, the U-joint angles must "cancel each other", meaning that an angle at the transfer case should have the same cancellation angle at the other end.
A common issue with taller lifts is to not have the joint angles cancel properly. For example, there may be a straight shaft out of the transfer case and through the mid-shaft bearing. If so, the angle of the second/rear driveline should have U-joint angles that cancel each other (complementary angles) on the second or rear shaft.
Many think it's great to angle or rotate the rear axle pinion upward to reduce pinion joint angle. That only works if the angle either 1) matches the angle complement at the other end of the shaft (which is impossible) or 2) the front end of the shaft uses a double-Cardan or CV type joint as seen in the photo below. Also see this Jeep XJ Cherokee article at the magazine for a single piece driveline and 6-inch long arm lift: http://www.4wdmechan...nsion-Lift.html.
CV Type Driveline.jpg 74.6KB
A CV/double-Cardan conversion joint at the front of a one-piece Jeep driveline. (This is a slip yoke eliminator kit or SYE approach.) Click on photo to enlarge. (If you cannot see the photo, join the forums, for free, and get full member access.)
Visualize a one-piece driveline. If the rear/pinion U-joint has little angle, the only way a lifted truck driveline will work is with a CV joint at the front of that shaft. The CV joint in this case has "self-cancelling angles". I will make the pinion joint angle 1.5-2 degrees. This slight tilt enables the rear U-joint bearings to rotate in their bearing caps. If you make the pinion and U-joint angle "zero", the U-joint will fail from lack of lubrication: The cross-shaft never rotates the needle bearings in their caps, and the joint quickly wears out.
So, beginning with your front shaft, the angle from the transfer case to mid-shaft bearing should be minor, just enough to rotate U-joint bearings. The rear driveline section U-joint angles must cancel each other (measure the same) if you have single-Cardan cross joints at each end. If a double-Cardan CV at one end and a single cross joint at the rear or pinion, put 1.5-2.0 degrees of angle on the rear U-joint.
Check your driveline angles and also the phase or alignment of the joints. If you have a single piece driveline with single Cardan U-joints, follow my guidelines for the cancellation of joint angles. A one-piece shaft with a CV/double Cardan at the front (SYE style) and rotated pinion at the rear should follow my guidelines for this type of shaft and joints.
U-joint crosses should line up with each other from the transfer case to the rear axle. If they do not, the driveline is "out of phase" and will vibrate, shudder or bind.
When you make these checks, the truck should either be on level ground or with the axles weighted on four stands (two at the front beam axle, two at the rear axle). U-joint angles are always with the truck "normally" weighted and spring heights at on-the-ground compression. You can check angles with an Angle Master gauge, I've even done it with an accurate protractor, plumb bob and level.
As a final note, you have shared that you're still running 3.73 axle gearing with the 37" oversized tires. This is enough to cause extreme take-off loads and maybe even the shudder you describe. The 3.73:1 gearing is marginal even with the factory tire diameters of less than 32". At your current ratios, the gearing is way out of balance.