Keep in mind that the 3 mins average time would be calculated from the non-bounces.... Adobe is not a heartbeat system... it's engaged time is a calculation between time stamps.... if a user bounces (which by Adobe's definition means a single server call in a visit), then there is no second timestamp available for calculation.
What type of site is it in general? Different site types will lead to different behaviours... for instance a news / blog site would have a tendency to have a higher bounce rate... people would see an article or blog post that interests them from a search result or social media site, etc.. they click in, read the content then leave...
Whereas an ecommerce site is much likely to have more pages / actions per visit as people are shopping, putting items into their carts, etc....
Understanding the nature of the site would help us to make suggestions about engagement.
In the meantime, have you broken down bounces by pages or page types? Does the site have multiple subdomains that might not be identifying the users across the visits properly?