We would be an over the cap, mediocre team struggling to make it to the 5-6 seed, with little hope for the future.
I think your definition of mediocre is different than mine. To me, mediocre is what we have currently - a team that isn't all that awful, but not good enough to make much noise.
My guess is that the Jazz, like most seasons with that lineup, would be battling for the 3-6 seeds and probably little more. I think, unlike past years, they could have locked down the 4th spot, though, because the west doesn't seem nearly as stacked at the top as it did between '07-'10 (to be sure, SA and OKC are legitimate contenders, but beyond them, it kind of fizzles fast). So, with a few breaks, a decent enough road record (Utah has the worst road record of any team battling for a legitimate spot in the Western Conference playoffs this year), the 4th seed could be theirs, though I don't think they would have been able to catch the Lakers. That would give them most likely a first-round series against the Clippers, with home court, and a probable series win (since, you know, in this reality, DWill owns Paul). Of course, that means they're most likely out in the second round against the Thunder, but I think with that team, it would be a fun series that could very well go the distance.
Either way, we'd be a lock for the playoffs, but the uncertainty of the future would be so pressing that we would probably feel the window toward doing anything in the playoffs was close to slamming shut.