4" is too much in my opinion, 2" max is what i like to leave. best bet for you mate is if you cant cut any more off that 4" joint put the blank on the floor and get a heavy hammer and hit one side of the interior lump hard (and i mean hard) at about 3 o'clock then do the other side then the top and then bottom. if it hasn't come out by then you'll just have to cut more of the connecting wood away.