Well the characters have access to nanotech so building the machine, using very advanced materials, shouldn't be a problem. As long as it operates without electric power.
Hmm. That could eliminate the problems, since with nanotech you could build the machine (in this case, a single-purpose analog mechanical guidance control computer) on a much smaller scale. Not necessarily on a nano scale itself, but maybe the size of (take your pick) a briefcase, pack of cards, or wristwatch. The best way to power it would be a wind-up spring. Really.
There are also concepts out there for nano-scale programmable computers, that would operate by (IIRC) the movement of microscopic sliding rods. In theory these could outperform modern logic chips. Since I suspect it would defeat the purpose of the scenario for the protagonists to be equipped with an arsenal of equipment that is indistinguishable from modern electronics except that it "works by nano," you might want to put some practical limits on the nanotech that is available.
Have you read Sean McMullen's Greatwinter Trilogy? (Souls in the Great Machine et. seq.) If not, you might want to, because some of your players likely will have. It's set in a no-electricity world with developing steam-age-level technology (railways, semaphor communications, etc.), and part of the plot concerns the disruptive effects of introducing an elaborate mechanical computer.
Respectfully,
Myriad
