I have the EIEPro and DM6.
The EIEPro has different drivers, but I don't believe that would make a difference in this case.
You have verified that you are getting audio I/O, so we know that is good.
You don't have to select the EIE MIDI input. That is the MIDI DIN input on the back of the unit.
Don't select
any of the MIDI outputs. That is giving you useless (in this case) options that are adding to your confusion.
You can leave both your keyboard and the DM6 connected to the EIE.
Don't swap devices to the same port, especially when the program is running. This seems to confuse Windows, which in turn confuses MC. I have seen the friendly name become associated with the wrong device.
Is your keyboard class compliant, or does it have proprietary drivers?
The DM6 is class compliant. That's nothing special, it just means it doesn't have specific drivers.
If you turn off the EIE MIDI output option, the instruments should not populate. That's fine, you don't need them.
Don't worry about drum maps just yet. They do not make sound, and simply direct MIDI note info to a synth.
If there is no synth, the map is a dead end.
Let's keep this simple for now.
It appears that MC6 does recognize the DM6 as "e-drum".
You say that MC6 does not acknowledge when you play notes. Does the left red light on the little keyboard icon in your task bar flash when you hit a pad? If so, MC6 is receiving data from the DM6.
Insert SI drums, selecting the MIDI Source Track, First Synth Audio Output, and Synth Properties Page options. Do not insert a simple Instrument Track.
Set the Input of the associated MIDI track to e-drum, channel 10( the DM6 transmits on ch 10).
Be sure to select a program in SI drums, or it will not produce sound. Click on some of the drums with your mouse to verify that you are getting audio output from SI Drums.
If you don't get sound, check to be sure the Audio Engine is on. It may not be on by default, and you will need to turn it on manually.
At this point, your signal path should be correct, and you should be getting sound.
Let us know how it goes.