Once we get reliable space craft to put things in orbit at a reasonable cost, they could carry barrels of radioactive materials up and put them in boxcars (used rocket bodies or prefabricated boxcars) which would be linked together like a train.
This is a very old concept but a viable one.
Then all it would take would be one rocket to pull them towards the sun. The sun’s gravity would do the rest and the radioactive material would be consumed.
Do you think that there could be any noticeable effect on the sun?