How would one go about sending a probe on an orbit that goes around the Sun in the opposite direction as most planets? Specifically, a rather high orbit - something like Pluto's. What happens to possibility of gravity assists and Obereth maneuvers? Would using planetary fly-bys make turning harder? Would it necessitate excessive fuel budget?
Plutinos are dwarf planets in 2:3 mean-motion orbital resonance with Neptune. There's a large number of Plutinos, and to examine them better, a fly-by mission would be very helpful. Now to examine a number of objects roughly scattered around a single orbit, a craft in the same orbit would be best - except flying in the same direction as Pluto, chasing them all would take a very long time. One flying head-on, would pass all of them in half their orbital period (123 years) in unpowered flight, much shorter if using gravity assists for "shortcuts" to skip from one to another.