Welcome aboard.

"Common ground" or "daisy-chained ground" is the way most arcade encoders are wired. (example
here)
- In plumbing terms, picture all the drops of water (electrons) coming from one bucket (ground), flowing through several decorative fountains that switch on and off (circuit), and returning to the bucket.
"Isolated grounds" is the way that the Mayfair encoder is wired.
- In plumbing terms, there are several buckets of dyed water. Each bucket has several decorative fountains. If one bucket's fountains are supposed to pump red-dyed water and another bucket's fountains are supposed to pump blue-dyed water, you don't want the red and blue water to mix or the fountains will all pump purple-dyed water and you won't be able to tell which color it is supposed to be.
There's a pretty good example of how to mod a Mayflash
here.
The "common ground" joysticks you refer to are the ones with a PCB and 5-pin connector. (4 directions + 1 ground)

The Happ Competition sticks have no PCB so each microswitch NO and COM tabs can be wired to the desired direction and desired ground.
Hopefully, there is enough room in the case for the stick.

If not, you might want to look at the Zippyy stick as a budget alternative to the Sanwa sticks.
Scott