I haven't switched stance foots since I first started riding. When I started I kept switching around backwards, so I tried riding right forward. ... and kept switching around backwards. D'uh!
Ambidextrous means equally adept with both left and right appendages (either hands or feet). Most people that are right handed are also right footed (ride with left foot in front). Some right handed people are left foot dominant (right foot in front). In snowboarding we do ride "backwards" so it's not a big deal unless your board is "very" directional. Most directional boards do not ride backwards much differently on packed snow. For me, I can feel the directional difference riding switch but it is less of a difference than trying to ride a board that is not tuned well. Where I can feel a huge difference is pedaling with the back foot out.
Stance changes often feel awkward at first and require a "breaking in" period before they become comfortable. I recommend you start your right foot forward quest with a +9/-9 stance angle and a stance width of insides of the heels under the outside of the hips. Try pedaling around the flats first (do a figure 8 path) and then take a run. Try changing your stance every run and at least try +12/-9, +12/-12, +15/-12, +15/-9. Pick one and then try changing your stance with one setting wider and one narrower. Don't worry about how well this works compared to your left foot forward riding. One setting will feel slightly better. That's the one you want to "break in".
One of my teaching maxims is that people have the same problems riding switch that they do riding forward. It's just that the problems riding switch are intensified. You may find that the source of your issues is a technique problem vs a stance problem. If so, you may want to work on the technique change riding right foot forward and then see what happens to your riding when you are left foot forward. Usually we work on technique changes riding weak foot forward and try to bring those changes back to our switch riding and technique "strengthening" riding switch and try to bring those changes back to our forward riding. But in "confused" cases, vice versa may work better.
I'm concerned about your comment about the range of motion for turning your head. The only motion you need is to be able to touch your chin to your shoulder (without turning your shoulder). If you that do that in both directions, you need to see a doctor.