Force amplifier into oscillation
You are right on track.  A spike in K or u are definitely cause for concern. Even if it doesn't cross the unconditional stability line, it probably will after considering part-to-part variation, temperature, ground quality, and other variables. Keep in mind that a well designed amplifier is not over stabilized. That would just be wasteful.  I mention this because it's probably possible to make it oscillate if you try hard enough, so limit your stress tests to practical conditions.

I would start by plotting stability circles at 50MHz and any other questionable frequency. You should be able to link a stability circle to the "u" spike and figure out what impedance might cause an oscillation. Take note if the impedance needs to be presented to the source or the load. If that impedance is an open or a short, your method should work. Keep in mind, an open at the end of a directional coupler will transform to something else at the s-parameter plane of reference.

I prefer using a signal generator and looking at the output spectrum with a spectrum analyzer. As you mentioned, directional couplers can be used to add source/load pulls to the setup. You are also correct to consider monitoring the drain feed. Sometimes you can tell an amplifier is oscillating just by monitoring the power supply. The drain current might fluctuate randomly, or hold steady at an odd value.

A few extra thoughts... Low frequency oscillations can often be blamed on poor decoupling in the bias T.  You could avoid adding an attenuator by adding some RC decoupling or an RLC on the output that resonates at the oscillation frequency.