Since it's only happening when front axle is loaded, that should eliminate just about everything drive train except backlash. If there is backlash in the CV axle for example when you are under load and hit a bump/dip you have that also for spring action to pay out slack that is removed on re loading the spring. I get very very similar sound from my worn subframe bushing in the back. It only happens under load and when I go over "dips" that partially unload the springs.

That mostly leaves suspention parts and that means look into Etsy parts get torqued under load. Mostly that means shock tower and tension struts. Do some unloaded prodding for loose joints.

Since the problem is only happening under torque lift one tire off the ground remove the wheel and apply as much torque as you can (you can use 36mm socket on the axle nut to apply up to 300 ft·lb CW or put a bar between a couple lugs and hub to add a lever you can push with your foot.

Push hard CCW then CW and listen and look for motion.

Recently people have traced weird suspension sounds to the shock tower bearing and even a broken spring!

Oh final thought:

I did a complete front and rear suspension refresh and I still ended up with an occasional while braking wobble.

Turned out to be steering rack. The reason I bring it up is that after i finally figured out that was failing, I noticed it makes a thump sound pretty darn close to your "pop".

If your tires are 255 or wider, power application on front axle will torque the wheels toe out and hitting dips will cause the same relaxing of the springy tension that could slap into the rack backlash (that's what's happening on my car now).

Have somebody turn your steering left and right while engine off and confirm you don't have excessive noise in the rack mine i didn't notice with engine running but when off very obvious.

Also: do your recreation test like the video and try it while steering up a curve both left and right. If the sound goes away more likely rack.

Do you ever get shimmy under braking, especially if just rarely ?

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)