"up to about $350 and add extra $20s and $50s & $100s"
1) I'm not sure why $350 represents anything other than opinion... but whatever...
2) Having been in a situation where (hurricane, power failures) cash WAS king, I'll never again keep large bills in my "stash." $5, perhaps $10, but no larger. Didn't like paying $20 for a normal $2.00 block of ice because "My register is down... can't make change..." I could have given him a $5 and taken a small hit. If I had a $5.

I recognize the argument that large bills are easier to transport and keep in your wallet/purse. Fine. But for an emergency stash I'm happy with packets of 1, 5, and 10 denominations run through my foodsaver vac packer. Tight little packets, tuckable in many places. And I like the many places idea.