Hi, I have the successor of the 34410/411, i.e. the 34465A with the same LM399 reference.
KS definitely made another mechanical design flaw, as the air flows across the reference circuit, creating electrical noise.
I've put a plastic box over the LM399 and aligned circuit, putting down the noise significantly. I have published this effect somewhere, but don't remember the factor at the moment.
It's also possible to replace the LM399 by a standard LTZ1000 circuit, as in the '470, further reducing the noise.
I the 34970A, HP made another mechanical design flaw. The fan is located on the rear of the left side, blowing inside. The fan is half blocked by the mains filter, and therefore creates audible noise. If it would run freely, it would be absolutely silent.
Check if anything is blocking the fan in the 34410A
Frank