At 7:08 it sounds like the motors spun up suddenly. I agree the clicking was the gimbal trying to correct and you can hear the brushless motor actuating in a reset too, plus the image jerks just a bit with the clicks.
It seems this sudden control issue is caused by a bad response to something the controller is detecting. You didn't lose power at any point as far as I could tell -- the motors didn't stop or even slow really. Since you never seem to have any control once this starts, I'm wondering if it isn't a case of the receiver losing signal and going into failsafe. I've read a lot of accounts of failsafe not being configured by default for enough throttle to maintain altitude or even a slow descent. It could be that after failsafe is triggered, the extra weight is causing descent and prop wash instability now when your quad had been going into failsafe in the past but recovered without you knowing. And now dropping through prop wash is creating instability the controller can't cope with, and it stops trying to re-acquire the radio (or can't with the tx running). Intermittent problems are notoriously difficult to find and correct. If it is dropped reception, it doesn't have to be caused by distance, or weak signal. It could be a faulty component in either the radio or receiver (or both) and/or momentary local interference on the same frequency.
If I had to offer something, I'd say, create a dead payload the same weight as all the FPV gear you added. Remove all that powered stuff, and hang that dummy payload on the quad and do some more flights. I'm just having a really hard time believing this is totally electronic, although I'm not convinced the FPV tx isn't also stepping on your receiver at some angles. If your quad flies fine after many tests with an identical weight, it's something else, or weight AND something else. The problem is, if the drop out wasn't caused by the tx, and the receiver still goes into failsafe and descends from the weight, you won't really know it isn't something in the receiver, or if the FPV transmitter isn't causing it sometimes ALSO. If intermittent reception is initiating the cycle of events, how the events progress is not necessarily going to change, and again, I think the cycle could have been initiated before, but handled without your knowledge. The one thing the dead payload WILL tell you if the problem does not occur, is that it is NOT related to weight alone. Once reception lock is lost, having the tx signal present may be preventing reacquisition now, where it reacquired quickly before, and may even re-acquire and recover WITH the extra weight. I'm just not sure how the controller responds to being orphaned -- what the logic is?
Unfortunately, you don't have a log of telemetry data on the controller, do you? (I thought your DJI was using the Naza lite). You said you checked the voltage though, so your radio/receiver is two-way? I thought they used Spectrum radios.
As for finding a quad in the woods, yeah, that is a problem for a lot of flyers. It is common to put a strobe or other tracker on a craft, or if you have telemetry, you have the last good GPS coordinates to start your search with. You can also load those coordinates into another quad with waypoints and search from the air when a ground search fails. A lot of forest flyers like to keep their crafts painted with bright colors for just such occasions.