Here is a skeptical blog post (by "Gimpy" over at BSG who is very tuned into cap questions) on the same issue. Note that it STARTS by cutting Redick, Illasova, and Bellinelli:
Revisiting the "How can we sign LeBron" question with the following qualifiers:
1) Pasecniks agrees to stay stashed
2) any second rounders and other stashes don't sign yet
3) Cap goes to $101m and rookie scale/minimum contracts also go up 2.02%
4) Our first rounders have signed for the scale amount and we end up with the 10th and 24th picks
5) Since we're signing people outright, we'd renounce the room exception to have space
6) We renounce our free agents
7) Embiid doesn't make first team All-NBA
Alright, here it goes.
How much cap space do we have?
$26,464,762
How much do we need for PG? LeBron?
30% of the cap is PG's max ($30.3m); 35% for LeBron ($35.35m)
How can we clear that space without impacting our core?
If we can find a way to get out from under Bayless' contract, we get up to $35,040,678 in space, juuuuuust shy of LeBron territory. Now, how would we actually do that? We could tie seconds to him or one of our firsts or maybe some other young players. For the sake of trades, unsigned draft picks don't count dollarwise. I don't think there are many teams with cap space this offseason and I'm not sure that many of them will be able to absorb Bayless along with additional money. Brooklyn is a team that has space and limited other sources for assets so maybe they do something like Bayless/24/Justin Anderson for a protected second. That gets us down to 10 roster spots so accounting for two cap holds puts us at $37,235,333 in space.
If we stop there and sign PG at his max, it leaves us with $7,767,423 for a player like Redick. If we stop there and get LeBron, it leaves us with $2,717,423.
Let's say it takes $7.5m starting to get Redick. How can we get LeBron and clear enough space for JJ?
Welp, here's where we run into problems. We ran the scenario above and we're at $2.717m, but clearing another $5m in space is hairy. We have a lot of guys on low $$$ deals and we're at a roster under 12 players. Cap holds for roster spots when you have fewer than 12 players are $832k according to my assumptions up top. So clearing a guy like Furkan Korkmaz's $1.740m contract is great, but you also have to tack on $832k in cap holds, so you're only clearing half of his salary if you dump him for free.
So dump the expendables; where are we?
Dropping Holmes, TLC, Furk gets us to $5.1m in space. Dropping TJ gets us all the way up to $5.875m. Dumping the 10th overall pick gets us to the magic $7.5m number we were looking for with us landing at a cool $7,642,125 in cap space after signing LeBron and dumping all of those guys (or trading them for future draft picks!).
Short summary to a long answer of a short question: if we want to keep all of our starters and Fultz while signing LeBron to a max, we have to get JJ to take a starting salary in the $7.6m range, dump everyone else under contract, and give up or roll forward our two first round picks. If we want to keep all of our starters, Fultz, and sign PG to a max while JJ takes that starting salary, dumping Bayless, Anderson, and the 24th pick gets it done.
If anyone is interested in an alternate scenario, like trading away Covington, let me know and I'll mess with my spreadsheet.
Another option that I didn't include above but should have:
We could clear room to get to $32,182,040 in cap space just by stretching Bayless. I'm reluctant to recommend that because then you're stuck with a little under $3m committed to Bayless this year and the next two years. But if you can't dump him for a reasonable price and you have an opportunity to add PG, it's probably something you'd want to do.