You're doing the right thing. Search by concentric circles around BDL (BOS, LGA, JFK), carriers and times of day. Needless to say, you need to then factor in the cost of your time and any associated local travel. Travel sites such as ITA can be helpful in locating deals using these methods.

I wouldn't spend too much time delaying here. 6/28 is just before a high-demand week (Independence Day) so lots of travel.