I've finally found the solution in my best estimation.
Since Ariza will leave that brings my estimated team salary down to about 79m instead of 82m. The Lakers can trade Chris Mihm, Coby Karl and Lamar Odom together in a package to the Kings for Ron Artest, Mikki Moore (6m a year), and SAR (6.5m). That amounts to 17.5m versus 21m coming in. That works with the NBA' s cap rules if I'm not mistaken. The Lakers would thus have a total salary of 83.5m not far off what they would have if Ariza were to stay. On the other hand they've acquired Ron Artest to be the final piece, Mikki Moore a very useful veteran who has little use to a young team like the Kings but plenty to us, and hope that SAR can at least became a useful player this year as a backup PF.
The Kings achievement? They get to deal Odom to a team like the Knicks for pieces such as David Lee, Malik Rose, and Balkman.
The Kings save 16m, gain a young power forward in David Lee, and young defensive stopper in Renaldo Balkman for one year of Ron Artest.
The Lakers next step now that they're at 83.5m is probably to sit still and hope that Farmar can improve in the next few years defensively. Next year they'll have three major expiring pieces in SAR, Mikki Moore, and Derek Fisher. Kobe will step out of his contract and receive a lesser deal over the long term to help the team. If need be the Lakers could also decide during the year to send Jordan Farmar, a re-signed Mbenga or the like, and Radmanovic to Chicago for Kirk Hinrich saving Chicago about 14m or so over the next few years and giving them a suitable PG if they decide to draft Beasley. For now though I'll just put the Artest only team:
PG- Farmar, Fisher, 2nd rounder
SG- Bryant, Vujajic, Newble maybe heck I dono
SF- Artest, Radmanovic, Walton
PF- Gasol, Turiaf, SAR
C- Bynum, Moore, Mbenga