Hi Connor,
Two thoughts to add to the good comments so far:
* Mouthfill allows you to relax the chest much, much more than any sort of classic frenzel (drawing air up from lungs each time). The trade off is that you do have tension in your mouth/jaw/cheeks. And as Bill and Eric caution, it is a whole new experience that needs time to get used to. I am still in favour of the longer bottom time at relatively shallow depths as a way to ultimately realize greater depths on FRC.
* To do a really good mouthfill, tilt your head up (in the direction you are going). If you put your chin to your chest too soon, the compressive forces on your mouth/cheeks tends to drive the air back into your lungs, stomach, or mask uncontrollably and can lead to losing a good mouthfill.
Kars' advice on alternating mouth and nose breathing to isolate the soft palate was what worked for me, as well. I did it by breathing 5 in/out through my mouth, then 5 in/out through the nose, the 3/3, then 1/1, then switching nose/mouth (ie. with soft palate control without moving air). Listen for a clicking sound as you move it open/closed.
I think the mechanism of being able to go deeper with an effective mouthfill, whether you are ready for it or not, is that your body spends more time in a state of negative-ish pressure on the lungs, especially if you're taking a shallow mouthfill, too. As long as the dive itself is gentle, this becomes a great stimulus for adapting to the pressure on the chest wall and its tissues (and perhaps blood pressure?).
An interesting equalizing dive profile to try (Tyler coined the term "Circle Equalizing" a while back in a conversation), is what I generally do when I dive for fun:
0-5m instinctive equalizing (usually hands free)
5m mouthfill
15-20m mouthfill when the first one is feeling challenging to maintain and that's the last one
For a deeper dive:
0-10m on one mouthfill
10-15m another one
20-25m last one
What this type of diving allows is for less tendency to activate diaphragm muscles with frequent frenzel (less in the way of sudden strain on the chest, trachea, lungs).
Diving with mouthfills like this means that you are usually at RV or really close, even at shallow depths. So if you have long duration dives, even if they are recreational, especially with relatively slow descents, (IMHO), you have more time to allow your body to adjust and adapt.
I remember after a span of diving this way (maybe a month?), my ability to do deep frenzel jumped by a good 15m on FRC.
I think the reason FRC works so well with the mouthfill when you have access to at least 10-15m of depth, ideally 20m, is that you spend way more time near or beyond RV, but, getting there is much less stress on your body than negative pressure dives or typical line dives can incur.
Pete