I have 4 LED flashlights which I run with NIMH batteries. They have not yet required a recharge in SIX YEARS.
Current drawn by the Paperwhite is from opening the unit and turning pages - NOT from the LED use. You can keep it at the maximum of level 24 and not change the battery life one iota. Dumping large numbers of ebooks on it will drain it fast due to indexing current use.