I'm pretty sure the noise is picked by the tubes themselves: If I place my hands around the tubes, the noise stops. If I pick the amplifier up and lift it above my laptop, the noise stops.
I'm guessing the mesh I used is too thin and has too many holes in it to effectively shield 2.4Ghz. I tried adding caps to completely close the cages, it helps, but the RF still gets trough. From the little information I can find about RF shielding, it seems that the only efficient way to shield those high frequencies is to use a solid sheet metal. I think the best option, short of enclosing the tubes inside a metal box, will be to reposition the amplifier relative to my laptop. Right now they are less than a foot apart, with a direct, unobstructed space between the laptop's WiFi antennas and the tubes.