Well I've had a good search around, and there are plenty of E350 and E450 based mainstream mini-ITX boards including:
- Gigabyte GA-E350N
- J&W Technology Limited JW-E350M-GT
- ECS HDC-I2
- ASRock E350M1/USB3
- Asus E45M1-I-DELUXE
There are also lots of custom form-factor boards which are difficult to find purchasing info for and/or are much more expensive.
So, I think my best bet will be to look at buying one of these boards.
The next question is, just how 'open' is the E350 / E450 platform? How well is the hardware supported by open-source Linux drivers? Can I run Linux (and use all the hardware features) without needing to load binary drivers?