I had very similar rough idle condition that would disappear at 1K rpm or when AC compressor was engaged. The problem turned out to be a cracked valve cover.

After replacement, I did a quick 440 mile turnaround trip between Dallas and Houston averaging 71 mph and 23.5 mpg with no more rough idle. It was a surprising solution.

2002 X5 3.0 318,400 miles
2014 428i 26,000 miles

2004 325i sold at 123,600 miles
2001 325i sold at 66,000 miles

1970 Firebird - Under restoration