Alright, I attached the mechanism I in my mind. The only reason I think it's not a radical mechanism is because the chiral center stays the same.
I also provided a reference in the attachment below, which should be strong enough to support my idea.
First of all, I believe the AcOH is simply used to activate Zinc powders so that zinc oxide coating could be removed. It may also help zinc dissolved in organic phase.
Then, metallic zinc insertion happens since the zinc is activated by acid. After the step i), the zinc complex is the intermediate which goes into next step.
After tBuOK added, it not only removes the acidic hydrogen on MVK but also removes zinc-halogen moiety in order to create another carbanion (see attachment below).
And eventually the ring closes.
The key difference is this.
The chiral carbon in mechanism you proposed is sp2 hybridized in the transition state, which will lead to recemic mixture eventually.
The chiral carbon in my mechanism is all-the-way sp3 hybridized, this will prevent recemic mixture.