I definitely like the idea. The simplest starting point would probably be to use the simple "like" system built into the forum. We could set some fuzzy threshold for which ones get picked up and made into blog posts.
If you're thinking we would automatically display popular forum threads on the site, that might be a little trickier. Since the site is purely static, we'd need to set up some kind of automatic build (not terribly difficult, just something to set up) to regenerate it on whatever schedule we want to shoot for. Other options might include something like a weekly highlight of popular forum discussions. We could either script it and just make it part of a weekly build, or we could turn it into a recurring blog post where we can add meta-commentary about the projects and why we think they are worth reading (while pointing people to the individual threads for more info/discussion).
As I wrote the paragraph above, I started to like the idea of turning it into a regular "column" on the blog. It serves double duty to promote interesting forum discussions as well as get us into the habit of trying to post regular content on the site. It will also be easier for other sites to pick up our RSS feed for a given highlight post and either re-post it on their site or link to us than it would be for them to pull the same data from the forum (I don't think there is an RSS feed extension for Flarum at this point).