If it looks like some of the teeth on the sprockets are shorter than others, that was on purpose to assist with shifting.

I’ve done what was suggested by vrktyg (a la Sheldon) to HG cassettes sprockets and it works beautifully. 7s HG still exist and typically don’t use spiders for the largest sprockets. Just be sure to keep the 13t threaded sprocket.

What kind of hub do you have on your wheel?