I've noticed that when some of my old questions get bumped due to edits or re-taggings, they often get new, good responses. There is nothing special about my questions. This means that in general, if we were to revive some old, good questions, they'd probably drive some fresh, good new answers.
Your observation that bumping questions often leads to fresh, valuable traffic is quite true. In fact, this was realised early on in the history of StackExchange. The idea of bumping questions that might need more eyeballs is explicitly implemented in one of the functions of the Community User. If you take a look at the homepage, it's usual to see several questions up there which were last edited by this special user.
As for how and when questions are automatically bumped, see for example the discussion here: Community should discriminate more when bumping unanswered questions. There have also been other suggestions for ways this could work.
With regard to frequency, it's a delicate balance to get the right amount of churn of old questions, without losing new ones too quickly. If there are too many old questions, or they aren't interesting to answerers (because perhaps they have been answered very well already), then these can have a negative impact on the site.
I don't know exactly what the rate of churn of old questions by the Community user is for our site, but in my opinion it seems reasonable. I don't particularly see any need to increase that. One of the things I'm most proud of with this site is that we have a very high answer rate of 98%, which suggests that most questions get a pretty good going over first time around.
I doubt that your questions are the only ones getting bumped. A lot of old questions make regular appearances on the front page.
Questions reappearing is something that probably best happens organically, as they are discovered by new members or found by experienced members.
Trying to manage a limited promotion of old material sounds problematic. I can tell you from experience that hits can drop noticeably when a large retag goes through.
We might get some, but I doubt the ratio of good new answers is that high for Old questions with previous Accepted or Upvoted answers.
First, let's clear what Community user actually does.
- Randomly poke old unanswered questions every hour so they get some attention
The Community user does not bump questions with an accepted answer, nor questions with an upvoted answer. You probably won't get many useful new answers by bumping old questions with accepted answers or upvoted answers. I only have my limited experience to base this on, so my sample size is too small (yours is too). You could run a query on data.SE for some more concrete data. Unfortunately, Boardgames.SE is in beta so you cannot run queries against it's database. Games.SE or other SE site might serve as a good alternative.
I am not sure exactly what should be compared. You might want to examine the total number of questions that a creation date of 1 year+, that have an edit within the last 3-6 months. Then look at the ratio of new answers to no new answers (determine how likely you are to recieve a new answer, or examine the total up votes for those new answers versus the highest answer older than 3-6+ months (determine how good new answers are). My guess is that you will find that new/late answers are pretty poor in general.