It's confusing isn't it?
I must admit I interpreted the MIDI specification this way when I read it (all those years ago)!
But OMNI on/off seems to refer to the channel on which the device can receive the "mode messages".
I have (somewhere) an ancient Roland SC-8850 which can receive polyphonic data on up 4 MIDI connections simultaneously, i.e. 64 channels (via USB 1).
And that works just fine the way you want to implement your guitar controller. It too is Mode 3 or 4.
Have you tried downloading the complete MIDI specification from the "specs" page?
Here:
MIDI spec.
You need to register first, it's free, then scroll down until you see "Download the Complete MIDI 1.0 Detailed Specification Document (1996)"
You can have it all for free as a pdf these days. (I had to pay for my printed copy.) :-(