OK, I just thought I'd update this.
I was having about 5 days battery life on my DXG. Nothing stuck indexing, whispernet off, autorotation off, about 2-3 hours daily usage (say 3 books).
Tried
waller4343's suggestion. Left it plugged in while it re-indexed everything, doing the "search for nonsense" while it did that so that I could see when it was finished (300ish books - 6 hours or so). Then unplugged and did a restart.
It's now 8 days and I'm only down about 2 bars on the power meter (75% plus left).
I don't know why, but this seems to have been the problem.
Thanks SO much.
I'm purposely NOT connecting it to power or PC for now because I want to see how long it lasts now.
Deleting the indexes is going to be a regular part of my Kindle Maintenance in future.
Not long after I got my DXG, I had a problem adding a couple of large books - 1 pdf & one mobi - and had to connect via usb to delete them. They were then reformatted with Calibre and re-added without problems. I'm wondering now if they were the ones that caused the trouble, maybe they left something in the indexes that the reader didn't like.
Most of my books are DRM free mobi format if that helps anyone.