Good point. It's possible to create cap space but only during the free agency by renouncing Favors and Exum so that's a moot point. Denver's pick is off the table then.
The available picks to move up are Phoenix #16, Milwaukee #17. Phoenix would probably take a protected 2019 pick plus a second rounder if they don't like who they can get at #16. Maybe even would have something like protected 2019 pick and Bradley (I don't think his value is particularly high now). Milwaukee pick is actually even easier because if you agree to send them a future pick and take Dellavedova's deal (2 years, about $10M a year) and send back Burks who they can actually use (and he has just one year left as opposed to two) then you probably have yourself a deal here. I doubt Milwaukee really want to add more young players currently so getting an upgrade in a backcourt position, some reasonably reliable shooting and a future asset should work perfect for them.
Picks behind Jazz that the team could acquire are maybe #24 from Portland (I'm their fan so I know the situation there, you are my second team) but that would require to take on Turner's or Leonard's contracts which are just pure evil, and maybe Celtics pick for future assets.
You get #16 or #17 and #21, take Huerter and one of the promising point guards (Okobo, Simons etc.) and you are sorted in terms of future talent to work with. Huerter would IMO play at the 3 and occasionally at the 2 when Mitchell steps up to the point guard role at times. He'd also help stretching the floor massively.
Or just go all in and absorb Noah's contract from New York in exchange for #21, Burks and additional future asset. New York will want to be players in free agency at some point in the near future, letting Noah go and taking on one-year Burks deal that is serviceable helps that. At #9 you can definitely get a proper talent to go along with Gobert and Mitchell. You give up the 2019 cap space though which is a worry.