SpaceflightMemes

You don't need to cancel the sideways motion at all. You just need to have the slighest motion toward the sun along with our orbital velocity which is being kept from being pulled awa by the suns gravity.

If you have the slightest motion towards the sun along with our orbital velocity, you will move closer to the Sun for one quarter of an orbit, before you start rising again. After half an orbit, you'll be higher than you were before. The difficulty in impacting the sun has little to do with the earth being here—even it it disappeared, the cost of getting to the sun would be basically the same

we don't care about a stable orbit or getting to the sun quickly at all.

The stability of the orbit is largely irrelevant. Anything near 1 AU is not likely to decay to the point where it impacts the Sun before the sun becomes a red giant and expands past the Earth's orbit. At that point, you can just leave your enemies on Earth and be assured that they will eventually fall into the sun in around 5 billion years