NOTES:
This chart shows the potential energy in the system, in the rotating frame; this chart will apply as long as nothing reduces or increases the angular momentum in the system. Pointing your rocket towards the Sun won't change the angular momentum in the system, so no matter how much thrust you apply toward the sun, you won't get closer to the Sun than Mercury.
So how do you get to the Sun - apply your thrust to diminish the angular momentum of the system.