Would it be possible to get to a retrograde orbit with a very close pass of Jupiter? Possibly multiple passes, possibly including Saturn passes as well?
I suspect anything's possible.
The main question is how long a mission you want (a lazy, looping trajectory over the course of decades, with the associated ground monitoring and support), or whether you have access to a significant propulsion system that can scrub quite a lot of your dV for you and accelerate the process. As another poster mentioned, we're talking about slowing down by >10 km/s and then putting it back on in the opposite direction.
At that range of course solar isn't much use, so for your power source you're looking at an RTG which means your maximum mission life is determined by the rate at which your isotope cools and electricity generation drops off (based on Voyager, gives you at least 40 years, but probably not more than 60).