After the failure at the tuner shop my son has decided that we should try removing the MSD equipment (control box & distributor) and switch back to the Chrysler electronic controller with the FAST distributor. I'd left all of the wiring in place but disconnected from it when we installed the MSD setup so it shouldn't be too difficult to make the change. The worst part will probably be having to notch the head to clear that FAST distributor.
If this swap doesn't cure our headaches the next step will probably be to re-install the MSD parts and disable FAST's timing capability. The technicians at FAST swore their system was fully compatible with the MSD equipment we've got but we've been unable to the timing stable when we've tried the two together. I don't know if the multi-spark is throwing their ECU fits.