Earlier quoted context omitted.
Getting into orbit would be rather difficult, as the probe would have have to match the planets velocity at perihelion. My instinct says it’s probably just on the edge of doable (although I’m not sure on which side), but I haven’t crunched the numbers. It would almost certainly need to be launched on a Delta-IV or Falcon Heavy class vehicle. EDIT: s/perigee/perihelion. I could say periapse and be neutral, but perihel…
It's difficult to believe that ten years from now, there'd be any serious options other than Starship and its future peers. (Incidentally, the Delta IV is already at end-of-life; ULA is replacing it with Vulcan and its Blue Origin engines. The final Delta IV-H launches are planned for 2023). https://spacenews.com/ulas-delta-4-heavy-down-to-final-five-...
With Starship this would definitely be doable, and I’m really optimistic about it; I just wanted to be cautious in my predictions.
I also wouldn’t be surprised if Delta IV’s life gets extended. Vulcan is facing plenty of development delays, and Blue Origin are yet to produce anything useful.