It turns out that clocking the instruction register with BITCLK wasn't such a good idea, because its transitions occur slightly ahead of RUNCLK, and this was leading to glitchy behaviour.
So I came up with another solution to the problem that the change to the IR clocking was designed to solve. The IR is clocked with BITCLK as before, and the Run Control subcircuit lets through a RUNCLK pulse during a Continue pulse.
Changes to main circuit
Changes to Run Control