@Whoops I’m having this exact same issue, I mean exactly. Industrial area, the problem is worse some days than others. I’ve tried everything. Please tell me you figured it out at your place!!
Some troubleshooting tips:
First, see if you can put together a means of quantitatively measuring the 10k noise, preferably one that has a frequency plot like an FFT analyzer. A battery powered laptop with a USB mic pre and FFT analyzer software should do it. You want to be able to see if the noise increases or decreases as you interact with the environment.
Next, prove to yourself that your analyzer setup is clean. Take the rig outside away from any source of interference and check that it has a low, clean noise floor with no indication of any 10k. You want to make sure your meter is seeing the noise in the studio and not its own noise.
Next, bring the analyzer into the studio, put a shorting plug on the analyzer mic input, then check the noise floor. It should be clean if the USB interface is well shielded.
Next, substitute a home-brew measurement probe for the shorting plug:
When searching for electric fields, a few feet of wire connected to Pin 2 of the mic input XLR with Pins 2 and 3 shorted together will do it. If your USB interface has an instrument input, you might try that since it will have a much higher input impedance than the mic input, and it won't load your probe as much. The wire would connect to the phone plug Tip, with Ring and Shield shorted. You may need to crank up the preamp gain. This "E field" probe is not direction sensitive, but it is very proximity sensitive, so if the 10k source is localized, this may help find it.
When searching for magnetic fields, use a "loop antenna" made by winding a few dozen turns of insulated wire around a suitable form. You can use anything nonmetallic as a coil form, but not too small, since you want quite a bit of loop area. I found that an empty gift wrap ribbon bobbin works well. Use a short length of mic cable to connect the two ends of the coil to Pins 2 and 3 of the XLR respectively, with Pin 1 connected to Pin 3. The more loop area and the more turns, the more sensitive the probe is; you might want to try some variations. This kind of "B field" probe is directional, so your FFT reading should change as you reorient the loop.
The most powerful debugging technique is to start turning things on and off, seeing if the noise increases or decreases in response. Unfortunately, if the noise source is in the surrounding environment, that might not be possible. Then you will need to "hunt" the source with your analyzer and probes.
If the noise is coming in on the AC power wiring, your E field probe should detect it when it is placed alongside a (nonmetallic) power cord that is plugged into the wall. The stray capacitance between the line cord and your probe will couple the noise energy into the analyzer. This kind of interference is known as "conducted interference" and is often very difficult to deal with, since it could be coming from anywhere in the upstream power distribution system.
The other kind is "radiated interference" where the source is broadcasting (intentionally or not) via some kind of antenna, and the wiring in your studio is receiving it. It is possible that this interference is being transmitted at some much higher frequency radio frequency (RF) and is being "demodulated" down to 10k by your studio gear. To find that, you will need a directional antenna and some means to measure the RF energy, like an RF spectrum analyzer. Your local ham radio club might be able to help you with that.
Good luck, and happy hunting!