I don't think it has the delta-v to go lower. Anything it loses to the solar wind on the flyby comes off the apoapsis, not the periapsis. Really messed up mission to Eeloo, returning the capture burn for Kerbin would have been around 2,000m/s and I only had half of that. After many reloads I managed to make it work: I put the encounter distance in the upper atmosphere and waited until the burn would complete a bit past periapsis to light the engine. The booster was destroyed by the heat just after the engine shut down, a good portion of my heat shield burned off but I came out of the encounter slowed just barely enough for capture. I turned around and waited. Every time around my apoapsis would drop, the periapsis stayed almost constant through many orbits. When my apoapsis was low enough I didn't expect to get another orbit I turned back around and went in.