I would put the stat back in. It won't cause your problem to be worse. If it did, it would just indicate a flow problem- either due to a bad stat or otherwise.

I would like to see a test with the stat back in there and the G-05 WW combo.

You are right that whatever is wrong might be the reason it isn't running liek it should. Problem in figuring out what that issue is that we can't narrow things down if the basics aren't what they need to be.