Is it possible to cut 2 traces on your PCB to isolate the filament chain ? If so, you could inject an AC supply onto the filaments.
As far as I can tell, the reason your tubes have varying brightness is due to the cathode being tied internally to the filament (I did not see a separate cathode pin in the datasheet, but there *is* a cathode in the tube). The voltage-difference between cathode and anode varies due to the progressive voltage drop across the filament chain, and consequently the current, hence brightness, will vary accordingly.
My best guess is that if you can isolate the filament chain, you would want to power it from a 12.6V RMS center-tapped transformer (or two isolated 6.3v windings). The center-tap would connect to the middle tube AND to your circuit ground. The 2 remaining windings would go to each end of the filament chain. The idea here is that the average voltage on any filament will appear to be 0 (gnd). If the brightness vs voltage of the tube is reasonably linear, you should see more uniform brightness.
I dont think an isolated filament supply would solve your problem; in fact, I think it would result in all tubes being dark because there would not be a complete path thru the anode.
I admit I've done very little experimenting with VFD tubes, and that was in the 1970's when Radio Shack sold them. But I did get mine to work.
The only other option I see is to use PWM as Tony suggested. This will allow you to make your brighter tubes dimmer to match the others.
Don't despair or give up! your display looks really neat.