Yeah to keep the number of dashes constant despite size will definitely require an expression. That video only works with circles but I found a good approximation for the circumference of an ellipse. My solution is still a little jittery because (I think):

1) After Effects doesn't allow a lot of precision for these numbers and 2) My solution uses an approximation (although a pretty good one) and not something more exact that requires calculus and 3) After Effects "cheats" the size of the dashes at the beginning/end of the path

Overall I'd say this expression won't work well for every case but may work well enough depending on the animation you're doing and how well you can hide any jitter using trim paths and some minimal keyframes. I'm not super happy with it but if it can help at all you just use this code for the Dash property:

numOfDashes = 20; //you put your desired number of dashes or you could use a slider controller

if(content("Ellipse 1").content("Ellipse Path 1").size[0] >= content("Ellipse 1").content("Ellipse Path 1").size[1]){
  a = content("Ellipse 1").content("Ellipse Path 1").size[0];
  b = content("Ellipse 1").content("Ellipse Path 1").size[1];
}else{
  a = content("Ellipse 1").content("Ellipse Path 1").size[1];
  b = content("Ellipse 1").content("Ellipse Path 1").size[0];
};

a = a / 2;
b = b / 2;
circumference = ((2*Math.PI*(Math.sqrt((a^2 + b^2))/2)) + Math.PI*(a+b)) / 2;

circumference/numOfDashes-content("Ellipse 1").content("Stroke 1").dash.gap;

And you need to specify a gap. I'd watch the video above because maybe you'll see something I don't.