Spitballing here:
The Champion’s actions within the maw (namely moving about it freely) involves activating the First Ones tech, the magic of which resonates within all living mortals. The souls of the deceased condemned to the Maw cannot access this energy/ability.
Powerful lore figures didn’t access this energy/ability because they were either unaware of it entirely, or blocked from accessing it. However, due to the Maw Walker’s repeated forays into the Maw, the magic that restrains this magic has been weakened, allowing for free movement within the Maw by those with the know-how.
This is based off part of a rework of the Shadowlands lore post I’ve been working on since October off and on (ultimately got scrapped), in which the whole “shattering of the sky above Northrend” had to be prefaced by N’zoth’s dimensional overlay of Ny’alotha onto Azeroth. This caused a weakening of the barrier between the cosmic planes of existence; the Void sees all but knows not the true path, and was therefore able to brute force its way to Azeroth. With the barrier breached like this, it becomes easier for others to follow suit. The next entity to do this was the Jailer, however he needed a surge of energy to do this, which was obtained by the influx of souls from the casualties of the Legion invasion and Fourth War, and not the shattering of the Helm of Domination (to the contrary, this was a necessary evil as, due to the surge of anima caused by the Legion, Teldrassil, etc, the Jailer was beginning to override Bolvar’s willpower. Yes, it frenzied the Scourge, but it kept that potent weapon out of the Jailer’s hands).
Similarly, the First Ones were able to freely move throughout the Maw, using a power that somehow links living mortals, titans, and world souls. Seeing as the entities in the Maw are either restrained or none of the afore-mentioned entities, escape from the Maw was impossible. Until the Maw Walker - a living mortal with power tied to the titans and a world soul - activated the First Ones magic. With the magic activated, the Maw’s grip began to weaken. With repeated outings into the Maw, it weakened further, again allowing those with the know-how to move about it.
Alternatively, our characters could be timing their movements with the Champion, or could be “hitching a ride” with covenant beings capable of traversing the Maw freely.