First experiment - swapped 11661B module with a supposedly-OK "just in case" spare I had picked up a long time ago (with understanding that the 11661B manual has an adjustment procedure to use when module swap/move occurs, which I didn't perform).
The output problem remains (fluctuating around 100-200 kHz below the set frequency), so taking this as a clue that the 11661B is not necessarily the problem, and starting into the fault finding tree in the 8660B manual.