This is my streamlined path through Act III:


Head right to meet Shadowheart's contact, the remaining tieflings, Orin in disguise, the Gur, and Orin in disguise again.
Go to the circus. Engage in various shenanigans. Ignore the body parts quest.
Go to the courier building. Pick up the mail quest and deal with Scratch's ex-owner.
Do all the things at the temple: scold Tara, pick up and advance the murder quest, exorcise the amulet.
Finish the courier quest.
Head down to talk to the gnomes.
Jump across the gap into the next area.
Flophouse: advance Astarion's quest and the murder quest.
Caress: advance the murder quest, talk to Raphael.
Dancing Axe: advance Jaheira's quest.
Head to the coronation and play coy with Gortash. Advance the Wyll/Mizora quest along the way.
Enter the lower city.
Kill red dwarf to stop further murders.
Get rooms at the Elfsong. Advance the murder quest by talking to Devella.
Go put down the murder tribunal, immediately followed by killing Orin to get my companion back. Screw that.
Side quests and character quests - get Minsc via Jaheira, confront Viconia and Cazador, resolve all the things at Sorcerous Sundries, break into the House of Hope, kill Ethel again, free the artist (maybe, if I feel like it), rescue Volo. Visit Jaheira's house if I'm taking my time. Avoid learning about Florrick's execution so the timer doesn't trigger.
Once everything else is done, head down to the Iron Throne, then take out the Steel Watch.
Save Florrick on the way to do Wyll's final quest.
Kill Gortash.
Off to defeat the brain.

And I long rest quite a bit to make sure I advance all those story beats and cutscenes.