All good responses. Putting the cylinder in a vice and just working the pick & bar can also help. I find holding the cylinder while picking can cause some stiffness. I had the same issue when I first started from doing a lot of shimming until I built up the endurance.
Out of everything posted, I think this is the gem:
I would also like to add that stopping and periodically stretching your hands once you have them warmed up will help with recovery and stamina.