I played a lot of badminton as a teenager and remember the ‘readiness position’ fondly.
On a road bike there isn’t much need for the wide stance as a form of control so keeping things as narrow as possible is a good thing for efficiency. In an ideal world the plane that your pedal rotates on should be exactly in line with your hip joint so that everything can move on that plane.
Greame Obree famously lay down on his bed and pedalled in the air. He noticed that his feet were much closer together than on a normal bike. He used the narrow bearings from a washing machine to make a very narrow bottom bracket on his bike, Old Faithful, which he used to break the world hour record.
Having said all of that, if you don’t feel comfortable with the narrow stance then using longer spindles or moving your cleats as far inboard on your shoes would be a good solution. Mountain bike cranksets are wider than on road bikes so if you can use one for a period of time, you might find out if it’s going to be a viable solution for you.
Mike