CONFiture
Please note in your second graph above, (the truncated version), That the a/c is shown oscillating in vertical speed up 1000fpm, down 1000fpm.
In autoflight. This is actual vertical speed, not selected.
The Selected trace covers it up, but I think it may be important.
edit: Sorry, this is repetitive, and Dozy squeaked my out. I'll leave it, so there is a record of my notation. Not like me to jump the gun before reading your complete post (as if).