Long ago, on QDX, we learned that L14 was capable of producing very large Ldi/dt spikes when the current through it changed abruptly at the end of a transmission. A commutating diode across L14 was proposed to absorb the spikes.
In QMX the presence of an envelope modulator was thought to moot that problem by gracefully winding down the current in L502.
However, rapid changes in load can also cause Ldi/dt reaction at L502. Rapid relay switching of an ATU almost certainly can do that.
I believe that may be the source of the high voltage spikes you observe when allowing an ATU to seek a match.