I suggest you wait a while before going for the 9600 to make sure there are no big issues with the player that would really annoy you. By then, the 9600 would probably be cheaper too going by what happen to the 9500.
Your 83 is not a bad player, holding out with it for a while longer shouldn't be too bad.
So far, the 93/95 doesn't seem to same issues as the 83. Beware that player/firmware problems happen to almost all BD players, just the nature of the technology. Switching to another player might just mean another list of problems.
Like I said, I would wait out a bit to see whether there are any big problems with whatever player you choose.
Currently, I am still using a slim PS3 for movie watching, which is very much problem free. But I've demoed Pioneer/Sony/Denon/Marantz/Philips/Oppo before over a long period of time. All of them very good. Hard to say which is better, just different. Which is why I still haven't upgraded yet as I want to do it right.
But I can tell you that right now I am looking at Marantz UD5005/7006 and OPPO 93/95. Waiting for more reviews/feeding back before I make a choice.