Are you saying that I should cut the binding the average length based
on three or four measurements, match the ends of the binding to each
end of the quilt side, and then stretch or ease the quilt center or
binding evenly over the distance between the matching ends?

unfortunately that's not the way it works, if you cut the borders to a
fixed size, determined by the quilt top so far, not the pattern, then
make the ends match, you should get a better result.

You've not mentioned whether or not you square up after quilting. I was
taught to do it this way, though I've seen many instructions that say
trim backing and batting level with top. I've not made many quilts, but
so far they've all been flat and this is what I've done.

cheers
Anne