Note: This is an off-season trade and uses the cap numbers for each team in the off-season.
Introduction
I just wanted to demonstrate that the 76ers, in theory, could outright sign Harden by dumping assets. I believe them dumping assets could be a relatively easy thing to do.
76ers
Ben Simmons + Tobias Harris + Danny Green + 1st Rounder for Harden
Collectively, if the Sixers were to dump Ben + Harris and then waive Green, they would have more than enough to outright sign Harden. If we were to add 1 first rounder to this deal, this would essentially be what they would be willing to trade in a S+T for Harden. So, can they get out from under these contracts in the off-season, while only losing 1 first rounder?
Spurs
Juancho + Walker + Bates-Diop + 1st Rounder for Ben Simmons
In order to fully absorb Simmons into cap space, the Spurs need to cut about 21.7 mil from their cap holds/non-guaranteed contracts. This is essentially the trade that the Spurs would need to make to get Simmons without sending any salary to the Sixers. Spurs could just waive Juancho, renounce Walker, waive Bates-Diop and then send out a first rounder for Simmons. Nobody in this trade gets any of the Spurs players. They are just renounced or waived.
Pistons
Olynyk for Harris + 2 first rounders
In order for the Pistons to take Harris into cap space, they only need to cut about 4.3 mil from their cap. Since I'm assuming the Pistons would rather keep their young players, the Sixers take back Olynyk, but that still leaves the Sixers with more than enough to sign Harden after dumping Simmons.
Conclusion
Seems relatively easy for the 76ers to clear up cap space for Harden this off-season. They just need to find wiling suitors who can absorb most of Simmons and Harris into cap space. Spurs would probably love Simmons for such a cheap price and the Pistons get 2 first rounders to take on a bad contract, which seems reasonable for a rebuilding team.