Well, technically most of the mission cost would be spend on Earth (paying Earth engineer salaries, and Earth factory bills), so the money never leaves Earth. The only money you are literally throwing is the material cost of the rocket and probe, which would be fairly low (the cost of a bunch of titanium (or whatever the rocket/probe is made of), silicon not worth measuring, the rocket fuel (which is surprisingly cheap), etc.

> get a better gravity assist from a single pass of the sun

No. The gravity assist is because of the motion of the planets around the sun. The sun isn't moving relative to itself. There are some other things you can do where the sun can help, but not a slingshot.