As t g mentioned,looking at ignition secondary starting with wires would be 1st step.
Have to ask why the need to run MSD ignition on top of DLIDFIS?
Properly wired/installed DLIDFIS is a reliable improvement over oe ignition .
Perhaps running DLIDFIS alone without MSD to separate the two systems to help diagnose and eliminate one source of potential problems.
Test your original Diamond coils 1st and use them instead of MSD ones. Should have approximately 3ohms on primary and 5k-8k on secondary and not leaking oil.
It is normal for any ignition coil to run warm to very warm.

I have used MSD components for years in modified ignition on muscle cars street driven and tracked and found them to be a worthwhile reliable upgrade. You must be diligent with maintenance on caps,rotors,plugs and wires as the extra current generated wears out these components at an accelerated rate. Should be using best quality ignition wires available to contain and convey that extra current to plugs.
Burning internals of even good ignition wires is not uncommon and can lead to drivability issues.
My experience with current MSD products has not been consistent,where they're made is a big part of this. QC issues,failures,particularly with their ignition coils are common. Those who state they have been running this equipment for a long time with no issue are likely using components that were assembled in this country before production shifted offshore.