Little update:
Decided to first just swap the pickups and change the Tusq nut before installing the push-pull pot for parallel switching.
Didn't want to have the guitar on the bench longer since it is my only electric and I have some time to play this week.
Also because I haven't found a schematic for volume push-pull parallel switching. Still going through the archives.
Regarding the difference in sound, I couldn't be happier! It is a massive difference. So much more clarity and dynamics.