 Two-layer measurement pattern for CNOT and x-axis rotations

An $R(\alpha )=J(\alpha )J(0)$ gadget with input Pauli frame $X^p{Z}^q$, angle-zero outcome $s$, and arbitrary-angle outcome $t$ uses angle $(-1{)}^{s\oplus q}\alpha$ and produces frame $X^{p\oplus t}{Z}^{q\oplus s}$. The CNOT gate gadget also updates its $Z$ frames without any dependence on incoming $X$ frames. Therefore all adaptive angle signs depend solely on angle-zero outcomes. Measure all those vertices first, compute every sign, and measure all remaining vertices in a second layer. The result is the desired logical circuit in a known Pauli frame. Computational output measurements can share the second layer.