I don't want to get into the debate over CPU speeds, have you considered running a benchmark app to see if this model is operating at a rate comparable to similar spec'd models?
Geekbench or Xbench can indicate if the Mac is matching others in performance. Ideally you would run it on a clean install to prevent background tasks causing issues.
This Mac sounds like it has been through a lot of repairs - personally I'd be looking at the price of newer second hand models, baked GPU's rarely make a Mac better in the long run, 'reballing' is a short term fix as far as I can tell and there are no new chips to fit to these boards.
Also try running Apple hardware test - see what that complains about, it may be more than just the battery if you are seeing performance issues.
How to use Apple Hardware Test on your Mac - Apple Support
If you don't have the original disks you will need to create your own bootable AHT disk…
https://github.com/upekkha/AppleHardwareTest
P.S. If you know your way around Linux try running it on this Mac - it will allow you to use the same tools to read the Mac's CPU speed.
EDIT: corrected second link