AFCI/GFCI breaker trips immediately with "extra" ground
The existing wiring is wrong

Obviously someone added the last/top switch and lamp to the end of the 3-way.  It was just a switch loop.  So rather than run proper cable, they misused ground as neutral, to free up a wire for always-hot.  Your last switch circuit grabs onto the bootleg neutral and always-hot. 

This wiring is illegal and wrong, and is inherently incompatible with GFCI.

The choke point is the /3 (4-wire) cable between the two 3-ways.   You really need:


always-hot
messenger
messenger
neutral 
ground 


Unfortunately you are considering this wiring "normal" on the logic that "it works", and figuring there is nothing wrong with it, so it ought to work with GFCI.  And expending a lot of brain power trying to figure why it isn't.   This has also poisoned your mind from having good discipline about separating neutral and ground.  They should never be connected (except at exactly one place.)

No brain power needed; there's a neutral-ground fault at the first (right, upstream) 3-way.  That's because neutral and ground are wire-nutted together.   

How to make this fiasco work

Run additional cable.  Between the 3-ways replace the 12/3 with 12/4, allowing hot, neutral, 2 messengers and ground.  Or install a parallal 12/2 to provide hot neutral and ground to the non-3way switch.  

How to make this fiasco work without running additional cable

Smart switches. You need a multi-way smart switch.  Whichever light is controlled by the 3-ways, its wires come into one of the 3-way locations.  That is where you put the "master" smart switch.  The "remote" goes in the other 3-way location.  The "choke-point" of /3 cable becomes: 


Always-hot
Neutral 
Smart switch control/communication
Ground


This is a relatively easy solution for a smart switch. We aren't a shop-for-me site but the right switches should be readily available.