Your understanding of the Space MIDI modes seem largely correct. It is possible (but of course unlikely) that a Space hardware issue is causing the problem.
I assume that if you connect the MPC directly to the keyboard, it acts as you expect.
If so, the problem may be cabling. Make sure that both MIDI cables work when connected between MPC and keyboard.
Make sure that the USB cable is disconnected from Space.
If you contact email@example.com, the nice man there will tell you how to run a MIDI selftest on your Space.