Here's one version of my attempt at it. I imagine you guys will hate it, but whatever.
There are 3 relatively major decisions for this offseason: Coby White, Nikola Vucevic, and whether or not to trade DeMar. Then to a lesser extent what to do with Ayo.
Also it is worth noting, I believe due to cap holds or some other rule, you can't sign all your external FAs first then use your Bird rights to go over the cap afterwards. Vuc's cap hold is 33M, Coby's is 22M, Ayo's is 6.2M. MLE and Biannual still apply for over cap signings.
Let's assume Drummond and DJJ both take their player options.
First Coby. In the same way as the rest have said, you let Coby get his offer sheet somewhere. If it's reasonable, match it, else he's gone. It's probably reasonable to assume he'll be getting at least the MLE (10.5M for non-tax teams). Let's assume he gets around 12M a year, pretty reasonable, but let's say we hate Coby so he's gone. There is no change to the committed salary which is currently 122M.
Next Vucevic. The common thought has just been dump him somewhere in a S&T. Issue is, there is probably not much market for Vucevic among teams needing a talent boost to get to the next level. Most teams have their center situation sorted. As such, I will do the unpopular thing and re-sign him. Let's say he signs for 3 years/60M (aka 20M per year). 142M for 23-24. Why does Vuc say yes? He is also aware of his market value and the lack of need for centers, 20M is only a minor dip in pay compared to his previous contract and he's paid until he's 35. I imagine you guys hate it, so it should work for him.
Next Ayo. Since Coby is gone it makes sense to keep Ayo on a relatively cheap deal. We have Bird rights on Ayo as well so if we had to go over the cap to keep him (ie contract value is more than 3M/year) that is not an issue. Let's say we "overpaid" Ayo 3 years/10M, 3.3M per year. 145.3M.
Next let's re-sign Javonte Green for the league minimum (~1.04M) 146.34M.
Finally we come to DeMar. In an attempt to restore the PG position that is in disarray I turn to one of two teams, the Toronto Raptors and the Portland Trailblazers. The reasoning here is that both franchises are in the same position as us, stuck in the 10-12 seed range and perhaps may be looking to make some changes. Portland as we know was eliminated from playoff contention and isn't looking like they can improve much. For Toronto, the rumors are that Van Vleet is looking to opt out of his contract and test the waters. With Siakam and Anunoby's contracts also coming up for renewal in the following season, Toronto is at a crossroads of whether they want to keep this core or not. DeMar's expiring contract may be enticing for one of those teams.
Let's try for Dame. He's owed 42.5M in 23-24, DeMar's 28.6M can only cover some of that, and of course we must sweeten the pot greatly. Now we get crazy. We offer Zach, DeMar, Patrick Williams, Dalen Terry, give back their weirdly protected pick, and some additional future lotto protected 1st in exchange for Dame and a S&T of Jerami Grant. Ludicrous I know. Let's say Grant signs for about the same as DeMar ~28M/year. Williams/Terry are owed ~12M combined making the difference in salary about 10M lower for the Bulls in 23-24. This trade works because Portland has trade exceptions from the Gary Payton II trade and the Josh Hart trade (~11M in total). 136.34M
Then going into 23-24 we have some nonsense like
PG - Lillard
SG - Caruso
SF - Green
PF - Grant
C - Vucevic
Bench - DJJ, Drummond, Ayo
Now we still need a bench, but we have the full MLE to work with so let's see what we can find. I look to Jordan Clarkson at a full MLE deal. 146.84M.
Then we sign some vet minimum and two way contracts to fill out the roster...let's go with TJ Warren, Will Barton, and old man Kevin Love. We'll keep our same random two way contracts Terry Taylor and Justin Lewis. For fun we can keep Carlik Jones and Marko as our GLeague guys with a roster spot who will never play. That'll bring us to about 153M or so.
Now we look like
PG - Lillard/Ayo
SG - Caruso/Clarkson/Barton
SF - Green/Warren
PF - Grant/DJJ/Love
C - Vucevic/Drummond
And some extra players who will basically never play.
What this does for us looks better than it does on paper
1) Acquire Lillard who is a borderline superstar, proven clutch player, one of the best shooters in history
2) Retain scoring/playmaking with Grant, a proven 20ppg scorer, above average 3pt shooter on volume (~37% over last 6 years) as well as keeping Vucevic in a similar role. Clarkson gives the bench a go to option who is also proven and can hit 3s on volume, additionally adding Warren who has the ability to fill it up and Barton who can function as a secondary playmaker.
3) Defense does take an overall hit, but we retain the swiss army knife of Caruso defensively, while hoping Green can come back to form as an energy player following the offseason. If he flops we have options at the 3 who provide offense. Still have Ayo, DJJ, and Drummond bringing similar contributions.
This group gives the ability to play in the modern NBA with the ability to take and make 3s at high volume. Good shooting can make up for a lot of things in this league. From there it is on BD to stop giving up wide open 3s in his defensive scheme, but even if not the offense should be able to carry most nights.