Here is something to try:
You are riding the trot without the stirrups well, use that position as your reference.
In an area where you can trot your horse with no hands on the reins and no stirrups. Let the horse go where ever it wants as long as it maintains the trot. Let you arms and legs relax as you trot. When you are feeling good and relaxed close your eyes. Ride a few strides and open your eyes and look at you feet position. I expect your toes will be pointing up and slightly out and your heels down. Adjust you stirrups such that when your feet are in the this same position you just clear the saddle when you stand in the stirrups.
After you get you stirrups adjusted at this point put you feet in the stirrups and just sitting there twist your leg to point your toes into the horse and you will find you will tend to slide to rear of the saddle. If you twist your leg to point your toes to the out side of your horse you will find yourself sliding forward. You will want to find a happy medium such that ultimately you will be positioned over the horse in your saddle in the same place with or with out the stirrups riding in balance.
Everyone's anatomy is different, some times our legs are not the same length and we have to adjust the stirrup accordingly, just keep adjusting the stirrups and trying them out until there is a place they feel right.