...My sitting trot with stirrups is decent- could definitely use some work, but in general I keep good balance and don't bounce around TOO much.
Without stirrups is a different story however... I can usually keep my balance for a few strides but then I need to grab some mane and steady myself
I can't seem to stay balanced without squeezing my lower leg when I'm sitting...
Sounds like you are tensing your legs when riding without stirrups. Squeezing with the leg will not improve balance. It may also be that fear of losing balance is causing tension in your thighs, making you bounce more and thus causing
you to lose balance.
Although this is in the English riding section, you might try using a western saddle for a few rides - preferably with a tall horn. Manes and grab straps, IMHO, don't do much to help restore side - side balance issues. There isn't enough leverage. With a tall saddle horn, you can adjust and keep going.
Once you do that, you lose your fear of losing balance, and start to have the relaxed, dead weight legs that for me are critical to successfully sitting the trot. I also found I had to lower my stirrups and let my legs hang down
. (This shouldn't be a problem without stirrups unless you still put your legs into the with-stirrup position). The weight of my legs keeps me from going up as far, so there is less bounce when I come down, and the cycle repeats until I can relax into the saddle. It also lowers my center of gravity, which always helps balance.
I find it helps to rotate my hip back a little towards my pockets. Not so much leaning back as relaxing in my hips and letting some of the bounce go into my buttocks instead of my bones.
Once I got the feel on a western saddle, it was easy enough to switch over to English. I could also shorten my stirrups some without bouncing, because I was no longer afraid of losing balance. [Note - in honesty, I can shorten them enough to lose the sitting trot. The higher my knees go up, the harder it is to sit the trot.]