THANK YOU for posting this thread!! DD has started doing the same thing and like yours has never liked tummy time. We are reducing the tension of the swaddles and making it loose enough that if she wanted to she could reach her arms out. Like you, I get tired of the nose pick (mine) when she is meant to be sleeping and the good ole boobie rub and hand down the top on the opposite side, not to mention the face wack!
The looser tension seems to be working well for us

Nae x