As a pet/learning project I made a data aquisition unit using an 8051
microprocessor and an EPIA M motherboard running a variant of Linux to
process and display the information. It all works but the EMI from the
EPIA M causes way too much noise to the aircraft radios. I have tried
shielding the whole device in an aluminum case with very little
improvement.

Any ideas on how to smother the EMI or some other small motherboard
which may not have as much an issue (as a test I took my portable
aviation radio and within 6' of any my home computers the same occurs
which gives me little hope)

Physically separate the offender from the victim, especially the point of
entry of the signals into the victim. Don't forget about coax cables, comm
antenna and things like that, not just the radio box. You could try
reorienting the motherboard 90 degrees in various axis.