My $.02. Reviewing the data, there is an "event" at at 11:00; it's more than a sound, as there is a divergence in Lateral Acceleration as well as the EGT's.
As Dwight pointed out EGT 3&4 fall off while 1&2 increase slightly. Immediately prior to the event, there is an increase in AMPS (7 to 20), and again during the event (7 to 20) -- suggestive of the boost pump being cycled -- the fuel pressure is varying wildly before, during and after this event. The decline in MAP is matched by the steadily increasing ALTGPS, indicating that the aircraft was configured for climb at WOT during the event.
At approximately 13:11, the OP/PIC pulls the aircraft into a ~2G, 5000FPM climb, followed by a ~.5G push over into a 3000FPM descent. At approximately 13:13 there is another asymmetric divergence of the EGT's coincident with a rapid reduction in MAP, RPM, Fuel Flow, Altitude, and an increase in Fuel Pressure w/out a change in Amps, at least initially -- OP/PIC chopped the throttle and headed downhill.
Ok - what causes EGT's to rise?
1. Delayed combustion - due to leaning mixture (fuel delivery, air delivery)
2. Delayed combustion - mis-/not-firing spark plugs
..and to fall?
1. No combustion - Stuck/Open exhaust valve
2. Mixture enrichment (too much fuel, not enough air)
Soooooooo...what to do. Since we now understand (thanks
@rvbuilder2002 - Scott) that the servo used (FM-200) can be sensitive to flow field disturbances which will affect fuel delivery, I would try two things and see if the reproduction of the event changes -- take a couple of flights with the cowl door left open, then similarly, remove the air filter for a couple of flights (with the cowl door closed) -- change one thing at a time.
As an aside - It would be helpful to understand the Amp excursions - is the OP/PIC manipulating the fuel boost pump or other high draw appliance (pitot heat, flaps, ldg/taxi lights); just looking for correlation here.