\begin{abstract}
Let $D_{2p}$ be the dihedral group of order $2p$, where $p$ is prime.
For every fixed $0<\alpha<1$, we prove that every subset $A\subseteq D_{2p}\setminus\{e\}$ with $C_\alpha\le |A|\le p^\alpha$ admits an ordering whose nonempty partial products are pairwise distinct.
Combined with the known small- and large-set theorems, this covers every subset size for all sufficiently large primes.
Pairing reflections reduces the products to partial sums with fixed parity-labelled offsets.
Two passes of block rotations remove distant collisions; bounded displacement allows the local condition to exclude the remaining collisions.
The existence of suitable rotations follows from Pham--Sauermann's subset-sum anticoncentration theorem, an affine-rank estimate, and a count of clustered collision witnesses.
\end{abstract}