Sure Backpacker will be along shortly..
Guess what... I was on a business trip and thinking "Mark1234 will be along shortly, so there's no rush..."
Anyway, I think there's two effects at work here.
One is the yawing motion which may unport the fuel inlet in the tank, leading to fuel starvation after, say, 10 seconds or so. (Note that an upright spin still carries positive vertical g's, so it's not exactly the same as what happens when flying inverted.)
Second is that the forward airspeed is Vs or less, and that there's actually a sideways component to the airflow. This will upset the windmilling effect.
It's the combination of these that, I think, will stop the engine.
When I started aerobatics and started getting confident in the R2160, I did a little test. Went all the way up to FL55 (the highest we can go in our airspace), set half throttle (2000 rpm or so), pulled the mixture to ICO and tried to get the prop stopped. In a full stall, with the sticks to the back stops and keeping straight with the rudder, the prop kept windmilling. I actually had to put the aircraft in a half-g humpty-like maneuver, so that I could fly the 30 knots or so that were required to stop the prop. And the subsequent dive was to 140 knots to get the prop windmilling again. (Or a quick application of the starter...)
My mentor later demonstrated the five-turn spin (over left), and indeed the prop stopped. I haven't done a five-turn spin over right.