Aye it's only from stabbing in the dark thoughts. I used to work with a chap who had a hobby of wrecking old BMW's, or "drifting" as he insisted it was, and after ruining 2 e36's with m52s in he moved onto an e39 with an m62, and that came with a similar steady noise at idle once warmed up, touch more clattery than Gav's but it had a degree of the thunder sound to it, sort of like air being shoved about out of time, and the running theory was the the valvework jumping with the slack on the "bad" bank, while the other side stayed nearer in time, giving the on off sound (not that we ever stripped it and looked, being proficient workmen)
That's partly what made me think of the thermostat swap, as the noise pretty much went away with a gruesomely thick 60 weight in it and an 85c stat (used to overheat with the original in it after a few runs). It did another 6-8 months or so before he ripped the nearside rear wheel and hub assembly off without trouble if memory serves, though.
Seems to go away somewhat with revs in the first vid, and a bad big end traditionally gets worse with load, sort of hard to tell without being there in the flesh though. Does the rattle worsen or clear up while actually driving about, especially foot down?