OK465:
But gaining unrestricted circling qualification on the LOC 27 circle to land 18R at MEM certainly neither prepares nor realistically qualifies you for this brand of circling approach, and doesn't distinguish between the two.
Amen to that.
Using your Butte example, the CAT C/D CTL HAA and visibility are greater than 1,000 and 3 so a Part 121 operator could take a 777 in there on a charter and do what you propose. The fact the PIC is not qualified to CTL doesn't matter because the greater than 1,000-3 gives him a pass on CTL qualifications.
And, Butte is "old TERPS" for CTL, so lots of luck in all respects.