I'm using the western saddle also for more security because she gets extremely bad.
Can you elaborate more on what you mean by this?
My leg also flies out in front of me and it's hard to bring it back when my pony gets "racy".
That means you are bracing with your stirrups for balance, instead of using your seat and legs. However, the TYPE of the western saddle you ride in will make somewhat of a difference on where your leg hangs. For example, most barrel racing saddle do have the stirrups set slightly forward, because that's the position that works the best for barrel racing (for most people). So just keep in mind that the saddle design may not fully encourage that heel-hip-ear alignment, but you still shouldn't be bracing with the stirrups.
You already do lots of "no stirrup" work and that's great. So when you do use the stirrups, visualize in your head and pretend you still don't have your stirrups. Envision "lengthening" your legs to make your heels touch the ground. Keep your weight back in the saddle, and use your thighs to keep your balance.
Does the horse have to have headset like they do in pleasure?
For horsemanship and western equitation, the rider is judged. So no the horse doesn't need to have a perfect western pleasure frame, but they do still need to be collected and travel correctly. If the horse doesn't travel nicely, that means the rider cannot effectively cue the horse, which will dock you.
Watch this video as an example from the AQHA world show. The horse's head is elevated higher than it would be in a western pleasure class, but the horse is still collected and listening nicely to the rider.
She's got a good headset at the trot after I work her a bit, but doesn't neck rein
Neck reining comes from your seat and legs. The reins are just the secondary cue if the horse doesn't first respond to your seat and legs.
Probably what will be a harder transition for your horse is going from contact on the mouth (English) to a loose draped rein (Western).