i've had a similar experience with a frame designed to contain the rear brake cable and housing within the toptube. once i found that i could access the toptube via the seattube, a little expanding foam in there did the job.

i would suggest a few dry runs on some scrap tubing just to get a handle on how much is needed.

BTW, if only the brake cable entrance and exits provide access, i think they can be used, in concert with the foam and some old brake cable and housing, to do the job.