Don't think the fuel flow thing is the cause; all the aircraft I've had the prop stop in have been injected, inverted systems types.
BackPacker, I don't have the Robin handbook to hand so can't say for that type, but I sometimes give my students a full power spin from a vertical climb to demonstrate that the recovery actions will work from other than an academic entry. The point of academic spin recovery training is to prepare people for a possible inadvertent spin from manoeuvre so I like to confirm that to them. Throttle on recovery must be closed, yes, but on entry shouldn't matter if we are being realistic.