  We derive a family of stochastic master equations describing homodyne
measurement of multi-qubit diagonal observables in circuit quantum
electrodynamics. In the regime where qubit decay can be neglected, our approach
replaces the polaron-like transformation of previous work, which required a
lengthy calculation for the physically interesting case of three qubits and two
resonator modes. The technique introduced here makes this calculation
straightforward and manifestly correct. Using this technique, we are able to
show that registers larger than one qubit evolve under a non-Markovian master
equation. We perform numerical simulations of the three-qubit, two-mode case
from previous work, obtaining an average post-measurement state fidelity of
$\sim 94\%$, limited by measurement-induced decoherence and dephasing.
