Don't lose your sanity for the sake of a few pounds.
You have mentioned most things that usually deals with mouse and keyboard problems, so you have gone through a list of elimination.
My wireless Packard Bell mouse is starting to play-up, due I suspect to age plus wear over the years. Just obtained two replacement mouse and keyboard kits (save on batteries, and problems associated with that), to see which suits me the most. One wired Advent C112 from PCW/Currys (£10) and one Logitech MK120 via Amazon Marketplace/ Shellbellquest (£11.09 delivered)