Curious to see what the result was?
I have an 06 TJ with 275k miles and the sound is most like yours. I've been chasing a misfire in cylinder 1 (only) and the plug looks fouled by carbon but no wet oil or anything. (Dry) compression showed 120psi on all others - but cylinder 1 at 65psi. Gonna do wet compression next - I got stopped by the rain too. And leak down if that doesn't tell me anything. I'm hoping it's not the piston, but I don't want to do a lifter, rocker arm, pushrod job unless it fixes the issue. Hoping the leak down will reveal the culprit or I'll be pulling the oil pan next as well - though I'm admittedly not a pro at this level of mechanical work.