I'm not sure how much this will help you, but when I do a hands free equalization the position of my tongue doesn't matter and my ears don't move. (I can wiggle them a little with the help of a mirror

) Hands free does feel a bit like yawning.
I come from a lifetime of swimming / scuba / snorkel and before taking a freediving class had never thought about equalization. I never needed to squeeze my nose while doing these activities. However, I immediately found that I wasn't able to hands free with my head pointed down!
Since then I have done regular hands free practice slowly switching my position from horizontal to angled down to straight down. The next problem I ran into was that I could only do heads down hands free very slowly. I practiced pulling my self down the rope faster and faster until I could hands free at normal finning speed for constant weight. Then I realized I could only go 10m deep before my hands free stopped working. So for all my safety dives I would do hands free to meet my buddy. Now I can go 20-25m hands free at speed and then I switch to normal frenzel with hand on nose.
Things I've noticed of note:
I can only do hands free for the first 45-60 min of a dive session then it just doesn't work for me anymore.
Hands free never pops the ears and there always seems to be a little pressure like I'm always a little behind on my equalization. This is noted by stopping decent and continuing to handsfree equalize and nothing more happens, then you plug your nose and frenzel or valsava and you get the pop and no pressure.
I think I occasionally pump my larynx to do the hands free. Like at the surface / first few feet of the dive. Then I feel like I switch to a continuous pressure equalization until I get to 20m where I start larynx pumping again. (maybe) Honestly I have a hard time telling what I'm doing most of the time.
I'm no expert and I get stuck at 42m with lots of air in my cheeks and unable to use it.
Good luck!