The modeling on the White Falcon works fine, nothing weird, normal JTV operation. GraphTech T-O-M bridge. Nothing weird happens when the strings move across the saddles, maybe due to the graphite saddles.
You will need to put a damper on the strings between the Bigsby and the bridge to kill string resonance, same as people without Bigsbys are doing with the stock JTV59/89 bridge:
I use a strip of scotch tape there and between the nut and tuners because it is nearly invisible but velcro or hair scrunchies or whatever will work.
I use the same scotch tape damping on my real (non Variax) Gretsch as well, at higher gain settings the resonance from the strings behind the nut and behind the bridge sounds terrible to me.
I do not use the White Falcon much, it sounds exactly like my Tele transplant (same Bigsby/GraphTech on that one, no issues) but the Tele has a great neck and is much more fun to play. I put metalflake binding on the WF body and neck and never finished working on it so the edges of the neck are pretty uncomfortable - needs more sanding and clearcoat, will probably get around to it eventually...
I have used it for a couple of shows, I chose red metalflake for the binding and Gretsch logo but later realized the guitar looks too much like a Christmas decoration/candy cane in red and white so I am planning to paint it black and probably change the binding to silver or gold eventually.
The couple times I did use the WF live I had not reinstalled the magnetic pickups, no pots or switches either, just a bunch of unfilled holes (I put all the Variax bits in a Radio Shack project box and stuffed the whole thing inside the guitar, all control of the guitar is done via HD500), got lots of "WTF is up with that?" questions about it afterward