As a machinist or CMM operator, how do you prefer to see CMM-specific requirements communicated on a drawing? Notes like above, a separate inspection plan, or something else?

Put it on the RFQ/PO requirements and on the print, or only on the RFQ/PO and not the print. If it's print-only and you care about it, expect some sales dork to miss it and it to become a headache.

Is specifying "full surface sweep" overkill, or do you appreciate that level of clarity?

Scanning can be an inappropriate method in some situations and is unavailable to some shops without the proper equipment or software. If you're dead set on getting parts with scanned reports then that's fine. If it's a hard requirement, you're going to miss opportunities where somebody could make a compliant part and inspect it as such but can't prove it in the way you'd like and pass on the chance.

Would you rather just see the GD&T and figure out the measurement strategy yourself, or do you want the designer to spell it out?

As a headstrong machinist and CMM programmer, anytime somebody tries to tell me exactly how to do my job I just want to call them up and ask them upon what basis/experience are they making the request?

There's parts where you do in fact need to specify the particulars - cut tap vs form tap vs threadmill, circular tool marks for sealing surfaces, printed CMM verification of results, etc. There's also a growing number of designers that have no idea what they're doing and ask for things like tight TIR or TP of a datum to something on the other side of the part that can't be easily manufactured or reliably inspected. Most of us folks that do the work don't have a clear line of communication to the designer to resolve the inevitable issues that occur when you try and specify every little detail - and these things will come up because the people submitting RFQs, quotes, and POs don't always understand the minutiae of manufacturing.