I can easily belive the Energizer E2 lithiums work well. At
two dollars a battery (I can get eight cheap alkalines for
two bucks...).

Are lithium available in rechargable? Lithium ion maybe?

not yet they keep promising that but it is so far vaporware

I don't believe they will ever produce lithium ion AA's at 1.5 volts.
A lithium ion battery in a common or non proprietary package like the
AA package creates a dangerous situation. If one tries to charge it
in a common or non proprietary charger it may blow up.

* They do make lithium ion AA cells at 3.6 volts