Even if you do decide to get a new mouse, you will still have to practice. There's no shortcut so I reckon you should just analyse your spinning and find out what the actual problem is. It may not be any of those things.
I'm gonna go with technique though. Your technique does not look optimal to me. It could be your arm angle/position, the pressure applied to your wrist, or how much you have tensed your upper arm, too much conscious decision... Who knows... I just know that when I spin, I'm just shaking my arm, but barely moving. Try finding an optimal position for your arm as a whole, angle, height, everything and just shake your arm until you get the motion right. We can't tell you what's best, because that's personal preference.
I for one, wish I could spin as fast as I can stir a cup of coffee/tea. One day I realised I was doing it really fast, and I just stopped and couldn't stir the cup anymore. It's like that story of a millipede... another insect asked the millipede how it walked with 1000 legs, for the first time in its life the millipede started to think about it and couldn't walk at all anymore.
So yeah, but in this case, you do need to apply both sides of your brain.