Sandman -
Lessons from golf would suggest the stance/set up can be extremely influential.
The old fashioned "hips and hands" hickory shaft swing as described most comprehensibly by Bobby Jones was the most similar golf swing to hitting.
This is one reason TEd Williams stressed the similarity of hitting to golf in SCIENCE OF HITTING, especially hip turn/hip cok and "getting your a** into the swing" (supposedly this was golf advice given to president Eisenhower).
Jones thought the high level golf swing pattern universals were best taught as a sequence of motions/functions which was invariable.
The 2 most important motions were the start from the stance (start of load motion) and starting the club down from the top (start of overlapping unload motion).
This means the stance and how it influences the start of loading is a crucial area if there is indeed significant "crossover" from the golf swing which I think there is.
While the hitting swing must be greatly shortened and quickened and made adjustable on the fly, the basic sequence of motion is the same for both.
The loading in golf consists of a turning back of the body lead by the hips AND a lifting of the arms. While these two actions (turn and lift) are blended in different ways by individuals, a UNIVERSAL is that the turn back comes first,THEN the lift starts.
Without the same sequence, you can not have a high level hitting pattern, you will be dead stop/no hands/low level hitter.
In hitting the turn back/inward turn needs to be relatively abbreviated and is interrupted then by the lifting of the arms which is accentuated in hitting as compared to golf. The lift is associated with cocking of the hip which requires "torso activation" of muscles and stops the hips from turning back excessively,coks the hips, and carries the body to toe touch.
The stance/setup should likewise be dynamic, not static. Lau's "rhythmic preswing activity" is a good description of a "universal" requirement of the high level swing pattern.
The hip turn back beginning from the stance and PRECEDING the arm lift is associated with some other "requirements" which may be more or less "universal".
Williams said "preloading" does not work/messes up rhythm. Do NOT start with the weight too much back and the hips already turned back.
Golfers have found the stance width and orientation of the feet to be influential as well. A "SWAY" back instead of a "turn" back is not fatal IF there is still the right sequence, BUT the timing of a back and forth sway greatly increases the chance for timing/sequencing error and loss of consistency.
A wide stance makes the turn back harder and a sway more likely. Likewise, having the back foot turned open as opposed to pigeon toed encourages a LONG back turn.
This suggests that a square or closed/pigeon toed back foot position would be good for hitting as well as a narrow stance.
Later on when you want to quicken the unloading of the short hitting swing,a WIDE stance for turning the hips is good.
How can we start narrow for a good brief turn back then get wide for a quick forward swing. Maybe a stride would work here ?
Then you have to also think of the effect of your base as it changes with the stride.
I am an arm action is king believer, but the lower body positioning and sequencing has a permissive/influential effect on how the arms feel comfortable working/ how the body gives support to what the hands/arms demand.
The back arm goes through a universal loading sequence for example that is the same in hitting and the overhand throw for example.The arm start holding the bat up which greatly shortens the swing as compared to keeping the lead arm straight in golf. There will be some pronation of the back forearm, then some internal rotation of the back arm and some raising of the back elbow as the back scap pinches, then some external rotation/lowering of the back elbow as the back scap remains pinched.
This arm action is far more acentuated/necessary in hitting for quickening the swing. Furthermore, in this torso or total body activated muscle mode, the back arm and front leg motions will need to synch. This synch is hard to do if the front foot is stuck on the ground. This is another strong argument for the "stride" style.
When the back arm goes through its necessary loading sequence, the front leg does the same.
Front foot square or closed after striding will tend to inhibit hips turning open with the swing unloading. It will encourage more of a loading hip turn back from the stance, BUT the influence is less than back foot position.
An open front foot after the stride foot is down makes coiling into toe touch and later rotation easier, BUT there is also a risk of encouraging sway/drift forward instead of rotation IF the hands did not load in behind the body AND the hips did not turn back when the motion began.
So, for example, a closed front foot as unloading begins CAN influence the hips to sway forward less and rotate forward more, BUT a FAR STRONGER CAUSE/EFFECT relationship is a body loading sequence that prepares for an inside out swing trajectory which is as necessary in hitting as it is in golf.
So, some summary points.
Stance should include some rhythmic motion.
Weight should be pretty even. Too much weight should not be on back foot. Hips should not be turned back.
Stance should not be wide enough to prevent a good hipcoil as beginning of negative move.
Stride is a good thing.Along these lines the not unusual 2 piece stride is instructive.
First piece of stride is to step back and in from open position to encourage starting swing motion from stance with inward turn/negative move.
2nd piece of stride consists of leg lift which helps establish the offcenter balance triggering torso activation which then proceeds to coking the hip as the front leg internally rotates/leads with the heel.
Then the "positive move" starts as the stride foot goes out while hips stay coked, "showing sole".
Then stride foot turns open as front leg externally rotates to start coiling the body going into toe touch.
Of course, you will not see this progression well unless there is a high level swing where the arm action is high level and demanding the lower body to synch with it this way, cocking the bat up,then forward,then uncoking the bat back and transitioning it into the swing plane.
The key to the timing of upper and lower body coiling is the synchronized external rotation of the back arm and front leg (as the hips and scaps stay cocked), just as it is in the overhand throw.
So anyway, back to the stance. Pigeon toeing the back foot toward the pitcher can discourage sway,BUT you must still make sure you begin the negative move with turning the hip back, NO TORSO ACTIVATION YET.
TORSO activation will then qickly follow as the weight gets entirely off the front foot, forcing "offcenter balance".
THEN the hips can **** with the synchronized internal rotion of the back arm and lead leg - bat coks up vertically as front leg turns so heel will lead as stride foot goes forward.
So when you think of stance, you need to keep in mind
Is there rhythmic motion ?
how wide?
how is weight distributed ?
where is head in relation to center ?
is stance open/square or closed ?
are feet open square or closed ?
how is bat held ? (grip is a whole nother story)
how will swing motion start ?
will universal load/unload sequence be supported ?
how will feet come down if stride ?
how will base transition if no-stride ?