I did exactly your second option on my '01 E53 with ~168k miles and original fluid:
"New filter kit with 1X drain and fill, then introduce X2 more staggered drain and fills later on (to prevent shocking it with all new fluid)"

The 3 D+Fs were done over a total of about 4k miles, and used two new filter kits.

I also drove like a granny for the first few hundred miles after the first D+F. From careful examination of the pan during each D+F, gunk _does_ get freed by the new fluid.

If I had to do it again, I'd do the exact same thing.

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2001 X5 3.0i, 203k miles, AT, owned since 2014