How far can you get? Do not mind having to change batteries often, they are rather inexpensive and easy to carry around unlike standard A-AAA sizes. What matters is the size and form factor.
When I read the title I immediately thought "there must be thousands of things"
Nick Gammon's power saving tutorial may be useful.
Oops! Yeah, I had already hit the page and some others, but I did not find them satisfactory. In fact, over the whole literature corps, anyone s conclusion should be: there is no acceptable way to power these things AT ALL. So I should add here then: under no-sleep-optimization scenarios.
Can you rephrase the question into something sensible?