Knowing that your only foundational pieces (Mitchell, Haliburton, maybe Holmes) are on team friendly deals for several years, I think you do exactly what OKC did. Deal guys like Barnes, Bagley, and Hield to other teams for their bad contracts and draft capital. Deal Fox for a larger haul similar to what the Bucks gave up for Jrue Holiday though ideally with higher picks.
Then you give the young guys all the minutes they can handle to see what you have there. Best case you have a piece (Queta, King, maybe Ramsey or Metu) that can be a solid rotational guy in the future. I think you'd see great effort but a lot of losses just because of the youth and lack of top tier talent.
You grab a kid like Banchero, Jabari Smith, maybe even Chet Holmgren with your own pick and let Monte continue to find good value with any later 1sts you got via trade.
You'd still have some veterans on bloated contracts for a couple years, but if the team's core next year was:
C Holmes/Queta (assuming there wasn't a great deal worth making for Richaun)
PF Banchero/Metu/Woodard
SF King
SG Haliburton/Ramsey
PG Mitchell
and another 1st rounder or two (Kendell Brown, Damion Collins, Ousmane Dieng, Roko Prkacin, Max Christie and Jabari Walker are some guys I currently like that should be available either late lottery or into the mid to late 20's)
would be a much more balanced and promising team than holding on to Fox, Hield, and Barnes.
Even with a great draft that team will probably be in line for one more lottery pick the next year before turning the corner.
I get Kings fans' reluctance to going this route. Yes, lottery odds have changed a bit, but more than anything I think it's the notion that the Kings have had countless lottery picks and have still managed to be bad. But for an example of what happens when it's done right you can look at the Sonics/Thunder and their drafts of Durant, Westbrook & Ibaka, and James Harden in three consecutive drafts.
OKC built a contending team primarily on the strength of those picks. And even when they had to make a decision between Harden and Ibaka and dealt Harden, they got a ton back for him. It's part of why they had the capital to trade for Paul George and part of why they now have a war chest of picks when they traded Westbrook and PG13. And that's after they lost their best player (KD) for nothing.
Lottery picks are the lifeblood of small market teams. They have to get high picks, but (and this is the point the Kings always miss) they have to HIT on those picks. I mean, even San Antonio's course was largely predicated on two #1 overall picks in Robinson and Duncan. They were masterful about roster building around those two (and later just Duncan) but the foundation were those two picks.
I doubt the Kings will go this route. But I don't see any other way to change the franchise's fortunes at this point. And barring a miracle deal from McNair, everyone on the team magically raising their game several notches, or a Giannis-like late lottery pick, I don't see anything else that's going to keep me from tuning out in the near future. I'm just about there as it is. At least a big gamble rebuild is a strategy.