"Launch today" is a very undesirable constraint for this goal. All of the probes that have escaped made extensive use of gravitational slingshot effects, which are only available during favorable launch windows.

https://en.wikipedia.org/wiki/List_of_artificial_objects_lea...

Long story short: they plan these out for decades at a time, and take your best shot when the planets align, literally.

We needed the slingshotting because until recently on-orbit construction was mostly a pipe-dream.

If you can build larger ships in orbit, relatively cheaply, you can go a lot more direct, a lot faster.

Even on-orbit refueling is a huge boon for orbital assist flexibility.

It's ineffective, you need more stages.

Tsiolkovsky's equation shows how much dV you get with a given wet : dry (empty) mass of a rocket stage. Very quickly it's becoming very inefficient.

Unless you are talking about some untested rocket that dumps empty fuel tanks in pairs. (Like in the dV book by Daniel Suarez).