Flats on a Jazz and Rounds on a Precision is the way forward.
I've had flats on both for many years and was already sold on flats on a jazz - as long as it's the right flats. But over the weekend I went back to rounds on my 30 inch shortie precision as I felt I needed a little more bite. I also went up a gauge to 50-110 Hi-Beams which allowed me to get a lower action too.
Hi Beams are too bright when new so I did the handcream thing before fitting them to just take the edge off.
Just have to decide which bass to take to rehearsals when they restart in 2 weeks time.