Please tell me that you don't have 6" blocks! Probably an add-a-leaf and 4" blocks out back? The add-a-leaf could be adding somewhat to the rough ride, it increases the spring rate some. As for the blocks, looking into a shackle flip would be a good idea!
If the shocks are maxed out (as in they are too short for the lift height), they shouldn't cause problems on compression as they have nothing but space for the wheel to go up. However, due to the fact that they are acting as your limiting factor on droop travel, they could be worn out due to the fact that they are not designed for that! So, worn shocks can be a factor too, check to see if any of them are leaking. Also, are they decent shocks or just worn out stockers? The stock shocks were never designed to handle a lifted 37" tired truck.
Front springs- any idea on manufacturer? Different companies springs ride differently, some even have options within the same company (like how Tuff Country offers EZ ride or HD front springs). A six inch lift is gonna be a little bit rougher (talking only about stock length springs) than a smaller lift kit anyway though due to the arch of the springs.
Last (and cheapest since air is free, LOL!) Tires- if your tires are over inflated, they can help contribute to a rough ride.
Or (expensive) Tires- more aggressive tires can ride A LOT rougher than less aggressive tires.
An example of running 37's that are pretty aggressive (Cooper STT muds, also used to have 33" swampers when it was sitting on 1/2 ton axles) and yet still having a VERY smooth ride (IMO)-
My K5 sits on a 3" set of Tuff Country EZ rides up front, an ORD shackle flip out back, and one Bilstein 5150 (14" travel) per corner and rides great! You can lower the lift height, trim the fenders, keep the tires you've got, and have a smooth ride!
Barring all those modifications, the first thing I would look at would be a good set of proper length/valving shocks, they'll make a BIG difference! Next would be a shackle flip to get rid of the blocks!