Good advice--I like the simulator. =b
I assume that you have a trustworthy horse? That said, work on your seat separately from reining. Therefore, I suggest riding "Western", with a slack rein while you work on your posting and your seat AND until you are comfortable with your new/old saddle. =D
While you walk you can check your foot position. Look down. You should NOT see your toes, but you may see the very, very tip of your toe. Lining up shoulder-hip-heel is more important in an English saddle for balance, than in a Western saddle, BUT, a good seat is a good seat regardless of equipment.
I'm sounding like a broken record here, but ride at the walk without stirrups for some of your 15 minute sessions. You also have better balance in an English saddle if you are sitting deep, and this will teach you what that deep seat feels like in this type of saddle.
Regarding reining, English asks you to keep a gentle contact with the horse's mouth. At the walk it will feel like "forward-back, repeat" due to the horse moving his head to balance. At the trot the head remains stationary. At the canter, it is again, "forward-back, repeat" to match the stride. Practice this at the walk, preferably at the end of a riding session, when you and your horse are more relaxed. Since you already ride, the transition won't be difficult for you. It will be a lot like a musician who is learning a new instrument--I've done that twice, now. With the first instrument you also learn to read and interpret music, but with the second instrument, it just comes faster. When the "English" saddle was used everyday (before the automobile) nobody thought much about how to ride--they just did it. Enjoy!!