Thank you for the photo. I see tons of Western riders who ride like that. In fact, I see it taught. However, if you look at how master western riders ride, you will not see this position. You will see a more upright, less braced position.
The bad part of such a chair seat is two fold. One;
Your weight goes straight down through your seat bones and ONLY there so is concentrated on the horses back in one spot rather than spread out over your entire pelvis and down through your thighs. Hores will be more likely to hollow out his back to get away from sharp seat bone pressure. Two;
If you brace into the stirrups you are not able to flow as well with the horse's forward energy. You are in fact bracing against him and he has to work just that much more to go forward. You are kind of "holding" him. You can feel your backward pressure against the cantle, no? He feels that as resistance.
So, in the above photo I see that you might need to lengthen your stirrups. The saddle itself may not have very good balance. The horse is very downhill in build and is carrying its' head WAY below its; shoulder tip. Isn't that a no-no in WP? I ride dressage so am not so familiar with WP. Your avatar photo in HUS looks much better position.
What kind of Western saddle is that? Can you do some riding just letting you legs hang down out of the stirrups? We used to be told to let our legs hang down, wiggle them a bit to loosen them and then just "lift" the toes from the ankle to pick up the stirrup. If you cannot, then the stirrup is too short and too far in front of where your leg naturally hangs.
My friend has a Crates saddle and boy does it have nice balance. I can post like a dream in it and my legs hang down in a very natural way.
Does this help?