Thank you for your suggestion.
I have however in increasing desperation and frustration found a solution that seems to work.
Downloaded a trial version of Deep Exploration, a notorious 3d conversion program. To my great surprise it does the job very fast! Opening my very complex model takes about 3 minutes, but then exporting a pdf or ai files takes about 30 seconds. And judging from what I have seen so far, the output is flawless. Literally tens of thousands of lines are outputted almost instantly. I am happy!
So this is just an advice for other users with the same demands I have. Deep Exploration seems to be able to do it.