I like the creative thinking, but it's a bit like suspension hubs in the 90s - hub shells supported by elasomers that isolated the axle. Bad idea as any vertical movement also means twist and deflection, not what I'd want in a bar-stem interface. Some carbon bars are suprisingly flexy, they may do the job you're after.
When i underinflated my tires after a puncture on the Capital Trail, it felt like wading through treacle when compared to my usual 30-40psi range (2.25 tires on flows). Also, larger tires weigh more where saving weight is most important, so if by adding a few grams here and there I can emulate that comfort without increasing rolling resistance and rotating weight, I see that as a worthy thing to do!
It may feel softer or sluggish but lower pressure tyres mean a bike with less rolling resistance off-road, plus the comfort is better. Pneumatic tyres are really great things : ) 2.25s on flows at 35psi is pretty high, no wonder you're looking for ways to add comfort..
Charlieacres makes a good point - most of bike comfort, or at least the greatest gains, comes from positioning. I believe the main driver for sus forks in the 90s was the need for comfort and control due to the daft head-down, bars over front axles position that most bikes put the rider in. What feels racy and fast isn't always actually fast, same as high pressure tyres off-road.
