I think the culprit is unbalanced connections and the SD Card. Eliminate either, and the problem is solved. I've sat next to a Taper with a Tascam DR-2D who suffered from immense static interference while my rig, a Sony M-10 was immune. The Sony records to internal memory, not an SD Card
I wonder if the new UHS-II SD cards, with a really fast write speed would eliminate write bursts and static.
SD cards are no more sensitive to RF fields than built-in memory. Both use the same form of serial interface (in fact, you can read and write SD cards with the SPI interface built into many contemporary microcontrollers). Most card sockets are shielded, BTW. A designer would have to be very incompetent to make an SD card interface RF sensitive - in fact it would not pass CE RF immunity regulations!
I do EMC tests regularly, and in my experience the main problem in this case is a weak shield of the unsymmetrical wiring. Some time ago when recording under a railway catenary of 15000V AC I had hum problems. I found out that the shield of the mic cable was not good enough. After replacing it with a better cable the problem was solved. Tip: measure the shield resistance from end to end with a good ohmmeter. I found that the ubiquitious ready made stereo cables from far east had a rather high shield resistance. Copper is expensive. Going to a show to record it too. So I built my own interconnects with high quality materials.
BTW I operate a portable transceiver for ham radio (4 times the RF power of a mobile phone) with a plug-in micro SD card to store audio and GPS tracks - and that card is built right
into a transmitter! Never had a problem.
Greetings,
Rainer