The closest way I can see to get something to be trusted is to start from a GNU approved laptop like [2] and add to it whichever modem you had on the neo9000 via usb... just as you said, but then you have this situation...
For something to be secure... there has to be a secure chain of trust...
-who creates the cpu? which kind of microcode has on it?
-video controllers? blobs? drivers?
-anything with DMA, who created your memory controller?
-are you sure about the media you are using to install?
-who creates the hdd? did someone "touch it" before you?
--what about the controllers on the hdd? ram? take a look on the latest technology and you'll see there is no way you can trust anything [0][1].
--anything with a controller... this is a cpu... this is something not being driven by the main cpu it's an attack vector.
"The potential of reprogrammable computers that, at a low level, run the code you ask them to doesn't seem to get through to most of the HN crowd" Do not generalize, different people, interests and approaches are part of how nature works, and remember we are as a friend said the "nature virtual machines".
[0] http://bgr.com/2015/02/17/nsa-hard-drive-firmware-virus/
[1] http://recode.net/2015/02/17/nsa-can-hide-spyware-in-hard-di...
[2] https://www.fsf.org/news/libreboot-x200-laptop-now-fsf-certi...
edit: format