This has come up before in several incarnations, along with curiosity surrounding the best time to ask questions (note, that's old data).
In reality, any time is the 'best' time because it's trivially simple for users interested in questions with a particular tag to follow them. You can't really count on front page visibility for more than a few seconds now due to the sheer number of questions that we receive in any given 15 minute interval. Put simply, Stack Overflow never sleeps and your questions are far more likely to be discovered by someone following a tag rather than seeing it on the front or questions page.
In extremely niche tags where maybe a dozen or so users actually participate, answers are going to be slow to come no matter what. Even if we showed you that 3 people on the site might be able to answer your question, we'd probably be lying, because all we could go from is the time that they were last seen. Also, would you be likely to post if only three people might be able to answer?
Just ask good questions, with emphasis on a very descriptive title. A good title can make or break your chances of getting the right person's attention. Also, use the 'share' links to promote them to anyone following you in the various spots that folks follow stuff, more lines in the sea so to say.
I can see what you're getting at, but this wouldn't be as useful as you think that it would at our scale. I sort of liked the idea a few years ago, but it's just not practical, much less feasible today. That's a bit of extra sweat for routes that see a lot of action, if we're going to make those work harder to render, there'd need to be a bit more payback for the effort.