This is a major question. From the player's point of view, this is "roll four (possibly more) dice to determine time spent". They don't seem to have any choices to make in this process, and that makes the process uninteresting. It seems a prime candidate for being condensed down to a single roll to determine if/when they find a solution.
yeah, that would be bad.
As a Trek fan and engineer kind of guy, I can make up plausible technobabble for what my PC would do that "could" solve the problem if it was on TV (or it'd be one of the things we already tried that didn't work, Captain)
The key to that isn't random lists. It's knowing what nouns apply to the topic at hand. The "warp core" does not apply to the security door. However, "Panel", "conduit", "power" does. Removing the panel, and rerouting the EPM conduit into the door actuator to overload it and force it open is plausible and sure as heck wasn't random buzzword bingo.
Much like a survivalist inventory moment, I'd rather the scene be set, given a list of system and parts nouns and see what I can come up with.
Perhaps from that, for a given "problem" you could roll up 1-4 valid combinations, and if I come up with one of them, the problem is solved. If it's close, you might give me a result that fails, but indicates I'm close (like the door actuator twitches, but it seems the EPM conduit doesn't have enough juice to force an override.)
This would help me feel like I'm actually solving the problem in Trek.