Double wrapping the bar can make a big difference. I have used another tape across the top and bends or I have also used a small piece of cheap camping matt closed cell foam.
I can relate to your pain, but you should know that the jolts on a cyclocross bike on the road are much smoother than those same bumps on a road bike. I was off road on some bumpy single track today wishing I had front suspension so I could keep up with my buddy on his Epic MTB. But, once we turned uphill and the rigidity and stiffness of my bike began to shine, he was left in the dust on the climb. Cyclocross bikes are a give-and-take (for me, they give much more than they take).
I find my Major Jake many times more comfortable than my TCR even when tire size and pressure is controlled for. It is so comfortable, in fact, that I am considering using it for Seattle to Portland (200 miles in a day) this year instead of the TCR.
My strongly held belief is that you will never regret choosing a cyclocross bike for commuting and will come to love it for many other tasks as well. It took me a while to appreciate it, but my Kona is pretty much my favorite bike of the stable. There is just about nothing it can't do. I have a 28 mile RT commute and often ride off road during my lunch break. There is no way I am hauling my double boinger NRS 28 miles per day just so I can ride off road. So I started testing the limits of the cyclocross bike. I find that I can ride serious off road trails even without having knobbies. I have very good success with the Michelin Transworld Cities 700X32's. They don't do high speed carves into sandy corners well but I am at peace with that for the increased speed on everything else besides descending.
On the commute, the Kona is just about (there may be some difference but it is so small that it is more of a hunch than a confirmed performance difference) as fast as my TCR and has no problems hanging with my buddies (and often smoking them) on their road bikes at speeds well above 25 mph (we were running 30 mph through downtown Boise and in spots on Fairview this evening with the 700X32's!!!!).
Cyclocross bikes are the SHIZNIT. That stiffness you feel will be a wonderful thing when coaxing every bit of performance from your panting, drooling self.b