After battery change, system becomes noticeably slower

In my experience, this is by design. Apple has intentionally designed their systems to run slower if on battery power on a non-apple original battery. I've seen it many times. One of the very many anti-consumer, anti-repair designs Apple does.

If you still have your original battery and some soldering skills, you can remove the control board from the original battery and replace it onto the new battery. This board has the "identity" of being Apple original and trick the computer into simply accepting the new battery and working correctly.

I would not recommend this if you have little/no experience soldering. While the task of removing this board is fairly simple, as far as soldering work is concerned, any work on batteries is very high risk and shouldn't be attempted without a good amount of experience and good safety measures on standby. That being said, it's not a terribly difficult job if you're careful and know what you're doing.

You'll have to pull back the black stickers on the little logic board to find the solder points. I'm attaching a photo of the solder points. This Apple battery isn't the same exact one as yours, but the attachments are very similar (I just don't have the exact correct one on hand right now).