For me it comes down to whether you want an MLB player or you want to say that you tried and the market wasn't right. I don't deny that you can't just throw prospects around willy nilly, but the odds on White, Blanco, and YDLS are that they won't make MLB. Maybe one becomes a part-time player. If you are really lucky, one becomes an everyday player or something more.
Maybe the Marlins need to add another player in to even it out some, but it's still in the ballpark. The rumors before the season had them interested in Ashcraft if I am not mistaken. I think you can stomach Ashcraft or Harrington as a 45+ or maybe 50 FV pitcher as the headliner of a deal, along with the lotto tickets.
Jazz is an above average regular who is controllable for two more years after this one. The only thing worth pausing over is that he does have consistency issues and he has slumped for a while this summer. He's not the solution to all of our problems who will be a huge impact player, though something like that upside is still present. But I think more importantly, he is the solution to a major puzzle piece that we do not have and will not have for the next 2.5 years. As long as a deal is within reason, which I would define as not involving Chandler or Johnson, or something like both Ashcraft and Harrington, then I am pulling the trigger.
My main caveat would be that if Mullins is available, there's a world where he brings you a good bit of what Jazz does except as a veteran and at minimal prospect cost (or baseball cost if you make a player for player trade, which seems more likely). I'm not sure I'd be into moving Chapman or Holderman for him alone, but if there's a prospect deal to be had there, or a bigger deal to recoup someone like Stowers or Beavers in addition at the cost of Chapman, I'm into it.