This type of round can be a bit irritating. It is pretty common so I do know how to deal with it. When the rings point outward, the thread tries to catch on them. I find that I can lay the doily across my hand, then fold it back across itself so it is out of the way. At least it works for me.
Round 10 will be easier. The rings connect to the round 9 rings. They are smaller so it should not take as long. My neighbor that I am making this four is really impressed with it. With half the rounds done it is right on 12" across.
I have been working round 9 while watching college football. My team (WVU) just won. It's a fine day.