Here's an idea that combines getting Harrison Barnes, giving Time Lord more minutes, and creating minutes at the center to be an attractive buyout destination for Aldridge. As a bonus, this deal does not require use of the TPE.
To Raptors:
Daniel Theis
From Raptors:
Stanley Johnson
2021 1st (Lotto protected for 1-2 years, then converts to seconds)
To Mavericks:
Tristan Thompson
From Mavericks:
Josh Green
WCS
To Kings:
Aaron Nesmith
Josh Green
Stanley Johnson
From Kings:
Harrison Barnes
To Celtics:
Harrison Barnes
WCS (absorbed via Kanter TPE)
From Celtics:
Aaron Nesmith
Obviously 4-team deals are difficult to pull off, at best. But this might give every team what they need. The Raptors and Mavs both upgrade their center position, at salaries they can afford, and for not ridiculous costs (protected 1st and a rookie who won't get development). The Kings get 2 rookie 1st round prospects and a pick, and don't have to take on long-term salary. The Celtics get Barnes, stay out of the tax, don't give up future picks, keep the Hayward TPE, and get a center who hopefully becomes third-string if LMA signs into the open roster spot, but is at least a serviceable backup if that part of the plan doesn't come to fruition, while giving Time Lord the starting role he has earned.