I recently viewed a map of The Baron's Keep and it showed spawn locations for both the friendly NPCs and the catapult and bomber vehicles within the level. They all go to the same place across runs, so the level isn't random by any means. Waves indicate a slight pause from one group to the next. Use this time to your advantage.

Aside from this, here is the list of spawns of cultists from all waves of the fight.

Wave I - Group 1 (3 melee, 2 archer) spawns on top of the hill upon the final boxes of dialogue from the Baron. They will progress to your player, so when you arrive to fight them, it's likely that they will have already come to the bottom of the hill. Wave II - Group 1 (2 melee, 1 archer) spawns between the two standing banners in the space between the bridge and the spawn hill. Group 2 (2 melee, 1 archer) spawns at the medieval cart on top of the hill. Both groups spawn simultaneously. Wave III - Group 1 (2 melee, 1 archer) spawns between the two standing banners in the space between the bridge and the spawn hill. Group 2 (2 melee, 1 archer) spawns on the bridge next to the castle. Both groups spawn simultaneously. WAVE IV - Group 1 (1 CATAPULT, 2 melee, 1 archer) spawns at the beginning of the flat plain right next to the spawn hill. A melee cultist will be advancing the catapult forward. Group 2 (2 melee, 1 archer) spawns at the medieval cart on top of the hill. Both groups spawn simultaneously. Wave V - Group 1 (2 melee, 1 archer) spawns in between the two standing banners in the space between the bridge and the spawn hill. Wave VI - Group 1 (3 melee, 1 archer) spawns on the bridge next to the castle. Group 2 (2 BOMBERS) spawns near the top of the 4th tree in from the castle. Both groups spawn simultaneously. Wave VII - Group 1 (1 CATAPULT, 2 melee) spawns at the beginning of the flat plain right next to the spawn hill. A melee cultist pushes the catapult forward. KOIICHI will begin speaking, and NURU will spawn shortly after near the 2nd tree in from the castle. Closely following is LANA BLAKE, who spawns at the first standing banner from the hill. Wave VIII - Group 1 (2 melee, 1 archer) spawns in between the two standing banners in the space between the bridge and the spawn hill. Group 2 (3 melee, 2 archer) spawns on the bridge next to the castle shortly after group 1. Group 3 (1 BOMBER) spawns above the first standing banner from the hill shortly after group 2. Group 4 (3 melee, 2 archer) spawns next to the medieval cart on top of the hill almost immediately after group 3.
Wave IX - Group 1 (3 melee, 2 archer) spawns on the bridge next to the castle. Group 2 (3 melee, 2 archer) spawns next to the medieval cart on top of the hill almost immediately after group 1. Group 3 (1 CATAPULT, 2 melee) spawns at the beginning of the flat plain right next to the spawn hill almost immediately after group 2. A melee cultist pushes the catapult forward. Group 4 (3 melee, 2 archer) spawns in between the two standing banners in the space between the bridge and the spawn hill almost immediately after group 3. Group 5 (1 BOMBER) spawns above the 4th tree in from the castle after group 4. Wave X - Group 1 (3 melee, 2 archer) spawns in between the two standing banners in the space between the bridge and the spawn hill. Group 2 (3 melee, 2 archer) spawns on the bridge next to the castle after group 1. Group 3 (3 melee, 2 archer) spawns next to the medieval cart on top of the hill after group 2. Group 4 (1 BOMBER) spawns above the first standing banner from the hill shortly after group 3. Group 5 (3 melee, 2 archer) spawns in between the two standing banners in the space between the bridge and the spawn hill shortly after group 4. Group 6 (3 melee, 2 archer) spawns on the bridge next to the castle after group 5. Group 7 (1 CATAPULT, 2 melee) spawns at the beginning of the flat plain right next to the spawn hill after group 6. Group 8 (3 melee, 2 archer) spawns next to the medieval cart on top of the hill while group 7 spawns in. Group 9 (1 BOMBER) spawns above the first standing banner from the hill shortly after groups 7 and 8. Group 10 ( 3 melee, 2 archer) spawns in between the two standing banners in the space between the bridge and the spawn hill shortly after group 9. Group 11 (3 melee, 2 archer) spawns next to the medieval cart on top of the hill shortly after group 10. Group 12 (3 melee, 2 archer) spawns spawns on the bridge next to the castle shortly after group 11. Group 13 (1 BOMBER) spawns above the first standing banner from the hill shortly after group 12.

And that marks the end of this wall of text. Travel to the Baron as soon as the last bomber begins the death animation and you will save precious seconds. Upon talking through more of his dialogue, the Bone Dragon boss will spawn. You know you've done it right if you defeat the boss before Asra Nox finishes his first line of text. You can then proceed as normal.

If you didn't feel like reading all that, I'll break it down very simply for you.

There are 3 places gangs of cultists can spawn, and 1 place each for the catapult and the bomber variants. Cultists spawn on the bridge, between the two standing banners, and next to the medieval cart on top of the hill. Bombers spawn above the 4th tree in from the castle, and catapults spawn directly next to the spawn hill right where the flat plain begins. The wall of text above is the order of which all these spawn.

As you might notice, cultists either spawn in groups of 3 or 5. 2 melee cultists spawn with the catapult with the only exception being wave iv. Bombers spawn by themselves with exception to wave vi. So there is a very simple method to all of the spawns and it really just takes time to memorize.

TL;DR - The Baron's Keep cageless is not hard. With a little practice, we can take the record clear to 3:20. I believe in us!