mini 2nd gen: Poor battery life even after replacement

I'm getting pretty poor battery life on my iPod Mini 2nd gen from eBay. I've replaced the battery twice now: an MCMConcepts one from Amazon and now one from andrd.shop on eBay. Storage is a 64GB SanDisk CF card. I was willing to accept one old dead battery, but not two--this new one even claims to have been manufactured 9/2024 at ~650mah.

The only real stand-out issue I know of is a slightly ripped ribbon cable for the click wheel near the connector. I couldn't find a replacement, but I found that I was able to create a shim that sits between the connector and the retention spring that will keep it working as it should.

If I put the iPod to sleep (Sleep in the menu, or hold play) and put the lock on, it will idle like that for around 12-18 hours before dying and requiring a charge. I've charged with a Memorex speaker dock and with a genuine iPad block on a genuine 30-pin.

I'm wondering if I ought to just get a big roll of kapton tape and start isolating everything--that seems excessive, though.

Any thoughts on where I should be looking?