Hi Martin,
Just an observation here...
My old mouse died a few months ago, so dragged out a (generic), new one.
It would not function correctly on my mouse pad.
I then tried another mouse (Gigabyte) & it worked "normally" & I was able to set it's options to suit my needs.
Now....I tried the 1st mouse again & found that I needed to place an white A4 sheet of paper on the pad & the mouse worked fine.
Maybe try the same & if it works....... paint the plywood white?
(The paper may get a little soggy........)