Starter keeps running

But THAT is not what you SAID

What you SAID was "go out, spend money, replace the relay"

I'm not belittling anybody. If you wanna go down that road it will get ugly.

Why didn't you suggest this in the first place? Amazing, you know all this troubleshooting skill, and yet..............

Because every time I've seen it happen, it's the relay.

Belligerence helps no one.