I agree that this saddle is not ideal for you, and will not support a correct ear-shoulder-hip-heel line. However I would suggest that rather than riding without stirrups (which is certainly a good exercise, BUT can actually promote gripping of the knees and thighs, producing a swinging lower leg, until a rider already has a reasonably secure seat and quiet lower leg), try riding in 2 point. Shorten the stirrups a good 4 holes, stand up in them, rest your knuckles just in front of the horse's wither, keep your back straight, look up and stick your bum out!
If your lower leg swings forward, you'll fall backwards. If it swings back, you will fall forwards. I have yet to find an exercise better than riding in 2 point at walk, trot and canter, to correct an insecure lower leg, and a gripping knee/thigh.