There are two things that come to mind. Grips, and gloves.
Depending on whether or not you use gloves, they do make some that have gel in the palms that may help reduce vibration some if you're not already using them.
Secondly you may try different types of grips, a couple worth mentioning would be the ESI grips. They're essentially made out of silicone foam and have several different thicknesses. I have yet to try them for an extended period of time, but they feel nice and I know a lot of people who ride them and have also heard good things. They can be seen here. They may be just the sort of thick soft foam type you are looking for.
You may also consider an ergo grip if you haven't. They won't help with the vibration as much as other styles but they may help by keeping your weight in the correct areas of your hand.
One other thing that came to mind that you may or may not be able to use are gel inserts. They're made for putting beneath road bar wrap but you may be able to use them for something if you get creative. They can be seen here but again, you would have to get creative on how to adapt it to a flat bar.
If your budget allows, you may also try out different brands or styles of tires, some thicker puncture protection (the 5mm rubber band rather than a fabric sheet) may help to alleviate some of the vibration as well. Depending on what you're riding I'm a big fan of the Freedom ThickSlicks. They have about double the thickness of rubber on the tread side compared to a standard road tire.