Welcome to the board!
I probably share similar views as those Bob expressed, but let me add some other thoughts.
During push hands, I understand and agree that during a forward push this forward lean would be beneficial, however since my center of gravity is slightly forward, I feel that if the person I'm pushing holds on to me, it would be very easy for them to off balance me forward.
I would say that it is easier, but it should not be easy. Every solution has advantages and disadvantages. What you choose to follow is what defines a style.
Both the Cheng Man Ching 37 and Chen Style I study have a very upright bow stance and much wider as well.
We have a way of showing the disadvantages of this position, but you can imagine pushing a car like this and get some idea. Again, this does not mean an upright stance is wrong, simply that it has advantages and disadvantages.
My Chen style instructor teaches that to counter someone pushing into you straight on, just sink down into your hips and this will reroute the opponents vector energy from the straight back into the back leg. And this seems to work without overcommitting my center of gravity in any direction but straight down.
I think these are good ways to test structure, but they do not really demonstrate how to counter techniques. As for "overcommitting", remember that the lean really comes from folding at the "kua" and rotating the torso forward. How much your center of gravity shifts forward is really a different consideration. To get the feeling, as the top of your body moves forward, make sure that your hips rotate back some. If you do our lean correctly, it should be quite difficult for someone to pull you forward.
I suppose my question is how does a forward leaning Yang practitioner counter a pull forward from an opponent if they are leaning forward after a push...
Remember that merely resisting the pull is contrary to almost all styles' interpretations of Tai Chi principles. Being able to resist may show good structure, but actually doing so is usually deemed incorrect.
In our push hands, we teach a "standard" Cai (pluck) application that more or less counts as a pull. If you do it successfully, both the opponent's feet will have to move and he or she will end up stumbling behind you. I have learned two or three counters to this technique: one involves squatting, another involves using Kao (shoulder stroke) with the shoulder or back, another involves using split/ward off. Each of these can also be countered. Whether these techniques work depends on the skill and understanding of the practitioner more than on the mere mechanics. Good structure is assumed.
...why are some Yang style stances so narrow in width?
I looked at one of the TTCS videos
. The practitioner looked very skilled. The bow stances looked narrower than what we use, but it is hard to tell from the angles. It looked to me that this was a way of emphasizing the stretching feeling the video talked about. I think our view is that narrow stances are more nimble and wide stances are more stable. We feel that shoulder width gives the best compromise. If I recall correctly, Tung Ying-chieh (董英杰) or one of his successors may have also advocated a slightly narrow stance, but I am not certain of this.
At a recent seminar I attended, Master Yang Jun talked at length about some of these issues. He said that various styles have different requirements. Sometimes the difference does not indicate that one is right and one is wrong, but simply that they have different approaches. Our style requires that the back leg in a bow stance give an idea of being straightened. If you do this with your shoulders squared and a straight spine, it will give you a feeling of tightness in the waist/lower back that is very bad for the flow of energy. To relieve this sensation, you can either lean forward or bend the leg. Either solution can accord with basic Tai Chi principles, but we choose the first one. I have some guesses as to why we do this, but they are only guesses and concern more training principles than meeting core requirements.
Unlike the TTCS video I saw, there are a few bow stances in which we do not lean. These are where we issue energy front and back and do not want to lean away from the energy going to the rear. In these cases, our shoulders are not square to the front.
I hope this helps.