I am working with a 14yo (she and her friend help my train) who has a chair seat. I have her ride my safe, 13 yo KMHSA mare at a walk for a full hour sans stirrups, before she rides my 5 yo geldings. If she cues and my mare breaks, it is at the amble, and gaited people here know how easy that is to ride. Lol
I don't think you can create a deep seat by just abandoning stirrups and ride the same exercises. MY instructor had plateaus that we had to reach before we were allowed to jump. At one point we had to drop our stirrups and post 3x around the track (inside arena) on both reins. This was after we warmed up, and we crossed our stirrups over, in front of the pommel, then took them up again for other exercises. This was obviously to give you a secure seat if you were on course and lost a stirrup.
Believe it or not, hours and hours this winter of just walking without stirrups will greatly improve your seat. If you think about it, you do grip the horse with your legs, thigh, knee and calf, only it is lightly and not a vice grip. We are like a sack of potatoes when we ride a horse. A sack of potatoes doesn't grip at all, and will fall off the horse if he tries to ride one. We "cheat" when we ride a horse with a saddle. If you can, try bareback on a really safe horse this winter, too. (It's lots warmer!!)