No, what you have going on is what happens to every stock, dual mass flywheel clutch....the springs in the flywheel that dampens the engagement are shot and the two plates are beating each other up. When they get bad enough, the truck will shake like you lost a couple cylinders.
It doesn't sound like you need anything drastic, but if you're going to do ANYTHING other than stock power, you want the OFE. That's the most common single disk setup we do.