Earlier quoted context omitted.
The sun's pretty big... And if you're worried about overshooting, you could probably lose a lot of velocity just braking against the solar wind.
While the solar wind gets stronger closer to the sun, it's an r-square law that balances the r-squared force of gravity. Fun fact: If a solar sail could be in a fixed position at Mercury orbit then it could also be in fixed position a Neptune orbit. Quoting from http://en.wikipedia.org/wiki/Solar_sail , the "total force exerted on an 800 by 800 meter solar sail, for example, is about 5 newtons (1.1 lbf) at Earth's di…
But space flight maneuvers typically use tangential or almost tangential thrust. Slowing down or accelerating the orbital motion will cause the altitude to vary, preserving the orbital energy and angular momentum. Placing a solar sail in a 45 degree angle from the sun will change the orbit slowly but surely, as there will be a little tangential and radial thrust.
I still don't think it's viable for throwing anything into the sun, though.