I think it's viable. There are no other forces acting on you. Set up the solar sail at 45 degrees "against" your orbit. You will slowly but inevitably spiral into the sun without burning any fuel.
If you have effective solar sail technology then all my calculations are thrown out the window.
If you don't, then the time to spiral into the sun is large. Figuring 5/64 N on 20 tons and an orbital velocity of 30km/s gives
t = v / a = 30 km/s / ((5/64) N / 20000 kg)
= 245 years to cut the orbital velocity
This assumes all of the force could be used to slow the waste hauler. As http://en.wikipedia.org/wiki/Solar_sail points out, the force is cos^2(theta) so the actual time at 45 degrees is
t = 245 * (sqrt(2)/2)^2 = 490 years.
The actual time will be smaller because you only need to hit the sun, and solar wind will get stronger. So, 350 years? As a wild-ass guess.
That same page points out that sails don't work much inside of 0.25 AU, because the temperature can exceed the material properties of the sail. Though I think if the apogee is inside of 0.20 AU it's good enough.
To make it worse, the solar wind fluctuates, so unless there's active control on the rocket, its orbit will be unpredictable over the centuries. When it's still near Earth orbit, or when it approaches Venus orbit, what are the chances of a gravitational assist leading to an Earth-return?
With 50,000 tons of high-level waste, and 15 tons per rocket => 3,333 rockets in uncertain orbits, the chances become much higher.
