Remember that magnetic field radiation is related to voltage. Your 2.5V filament lines aren't going to do much there. I would just twist them up.
Since you have two metal enclosures, you can put a metal braid over the whole umbilical and let that be your shield and the connection between the enclosures. That is always how I have done it. Of course be sure to get stranded wire for this and small heatshrink with adhesive to slip over each solder joint.
2A3 filament voltage drop could be an issue with what you're doing. If you switch to a 6.3V CT/4A transformer for each tube, you can full wave rectify that with a small resistor, then a cap. This resistor can be tuned to bring your filament voltage back up if the umbilical is driving you nuts. DC on the filaments will also lower the noise floor of the amp a bit, though honestly 2A3s are reasonably quiet as it is.