What are the problems with using the sun for Oberth maneuvers?
A number of recent papers have explicitly advocated using the Oberth effect near the Sun to achieve very, very high velocities. The only problem is heat. Conceptually, all we need is unobtanium to overcome the heating problem. The current lack of this fantasy material is of course a big problem.
Some of those papers advocate using conventional thrusters with a spacecraft passing very close to the Sun. An economical way to achieve this is to use a gravitational assist from Jupiter to cancel almost all tangential velocity. It's a lot cheaper from a delta-V perspective to go to Jupiter than it is to dive straight toward the Sun. The basic idea is to send a vehicle towards Jupiter, let Jupiter send the vehicle diving almost straight toward the Sun, and fire massive set of thrusters near perihelion. The resulting $V_{\infty}$ is huge compared to anything yet achieved by humankind.
Other papers advocate using solar sails in combination with sun-diving to achieve very high escape velocities. A gravity assist from Jupiter is not needed here. In fact, it's counterproductive; solar sails don't work very well beyond Mars' orbit. On the other hand, solar sails work quite nicely (and that's putting it mildly) inside of Mercury's orbit. All we need are solar sails made of unobtanium as opposed to a very thin layer metal on plastic so the solar sail can dive very close to the Sun, and voila! the solar sail can easily escape the solar system at velocities that make those obtained by the Pioneer and Voyager satellites look miniscule.
I'll try to dig up some references to these papers later.