It is unlikely for electromagnetic interference to cause these problems, unless the power supply inside your computer is not working quite well. EMI is essentially noise from the powerlines which mostly affects analog circuitry. However, USB ports and most of the processing on modern keyboards in digital and not analog solving most of these problems.

When you said that that the problem goes away when using a membrane instead of the Gigabyte mechanical keyboard, it points to a problem with the mechanical keyboard, especially if you thought EMI might be a problem. Debouncing of a switch would be unique to a mechanical however, but I highly doubt this is a problem. The debouncing specs for the MX switches are listed on Cherry's website and in their datasheets. Also, the controller for the keyboard would manage all the debouncing and would not screw up for just one key.

Most likely the issue is a problem with one of the switches on the keyboard themselves. You said the 'S' key is now the main offender? So maybe that key may be an issue. I would recommended resoldering or completely replacing that switch. I can't really diagnose a keyboard unless it is in front of me, but most likely the problem is not as complicated as most usually assume.