So I've been working with AVR 1-bit stuff over the last year as part of my PhD. I knocked up this incredibly basic 1-bit MIDI synthesizer in C a few months ago for a live performance. I've uploaded the code / schematics here if it's of any use. It uses the Arduino MIDI Library.
Example output here.
All of this is incredibly rough and originally made for my own benefit / reference. If you're using an Arduino you can ignore most of the schematic as this section below is basically the Arduino MIDI shield. You can build it yourself for like £5 (if not less).
The audio output circuit is rough, with no isolation, DC offset correction or lowpassing. Basically, just be aware that, while you can probably run a line in to most stuff, this is not 100% reliable or safe. If in doubt, headphones will do you absolutely fine. Also I personally love hearing the crackly 'brightness' of the upper harmonics, but add RC filter to taste.
Like I said, I knocked this up quickly so the code isn't commented, efficient or organised particularly sensibly. If there's interest in this I don't mind going through and commenting, but, Shiru, I think you've got a waaaaay better tone generation system in your other routines, so you could probably just slot it in (keeping aware of timer conflicts with the MIDI library, if you choose to use it). Additionally, I don't mind uploading better schematics, STLs for the 3D printed case etc.
Feel free to amend. At some point I was going to add pitch bend support, ADSR enveloping, vibrato and more effects, but it wasn't needed for the original project.
I'm a total n00b at all this, so any suggestions / pointers would also be very much appreciated.
EDIT -
If you fancy playing around with the synth, CC#1 is decay / sustain (it was originally two separate controls, but the difference between the two wasn't great enough) and CC#2 is 'volume', where the pin-pulse output is interleaved with silence. Channel 1 is pulse waves, channel 2 is PWM drums.
ANOTHER EDIT -
I know the Teensy can appear as a USB MIDI device, so you could ditch the outboard MIDI gear entirely.