At the same time, I saw a positive report about running OS/2 on similar mobo - Asrock Q1900B-ITX (I do not know how important the letter "B" is) but with OS/4 kernel http://www.os2world.com/wiki/index.php/Phoenix_OS/4#OS.2F4_Tested_Hardware_List
I do not think that it was working because of using OS/4 - so keep trying to change you settings.
This report does not mention USB, which is one of the problems I had left.
The J1900 mainboard is now in a FreeBSD system. The NIC works fine, using the same "re" driver that the Arca Noae MMRE driver is based on - which is slightly weird...
I bought two new mainboards to test - I hope to eventually find one that works completely

These two are ASRocks again - I have no particular like/dislike for ASRock, but my supplier Reichelt stocks a lot of them. They are the C70M1 and the QC5000M-ITX/PH. Both are based on AMD APUs, but the C70M1 is very cheap, and not very fast.
The good news first: The C70M1 system booted without any problems! Both the MMRE and the R8169 NIC drivers work. USB seems to work also. AHCI and ACPI works with default settings. The only thing not working (I haven't tested stuff like audio), is the PS/2 combo port. Connecting a keyboard works, but if you connect both keyboard and mouse neither work - but this is clearly a hardware problem, as the problem is also present in the setup utility.
The not so good news: The QC5000 system also boots (with both keyboard and mouse working), but networking is flaky. If you ping another local system, you get 15-20% dropped packets, and some take 2-3 seconds to get through. According to acpistat the systems runs in VW-mode, meaning nearly everything is on one shared (low) IRQ. I guess that could be the cause of the network drop-outs?
According to a changelog document on Arca Noae's website, the later ACPI drivers automatically switch to VW-mode, when they encounter a non-supported system configuration.
The C70 is about half as fast as the QC5000 (per core), so I would like to get the faster system running... The SysBench numbers (int/float) are 1911/129 for the C70 (dual core) and 6817/400 for the QC5000 (quad core) - so the QC5000 is about the same speed as the J1900.