Well, I've searched in the FAA document with a very telling name of
AIRLINE TRANSPORT PILOT
AND AIRCRAFT TYPE RATING
Practical Test Standards
for
AIRPLANE
It's the document that the Inspectors Handbook (which is a part of FAA Order 8900.1
Flight Standards Information Management System now) refers to. There's nothing there that requires that circling approaches should be performed at the circling visibility minimum values, only that it should be determined that the applicant "In simulated or actual instrument conditions to MDA, accomplishes the circling approach selected by the examiner", and, of course, the examiner might choose to "simulate" the conditions all the way down to the minimums. Otherwise, apart from the obvious requirements to stay in visual contact with the runway and not to bust the TERPS limits, the objective is to determine that the applicant (amongst other things irrelevant to this discussion):
[…]
8. Performs the procedure without excessive maneuvering and
without exceeding the normal operating limits of the airplane
(the angle of bank should not exceed 30°).
9. Maintains the desired altitude within −0, +100 feet, heading/
track within ±5°, the airspeed/V-speed within ±5 knots, but
not less than the airspeed as specified in the POH or the
AFM.
[…]
BTW, 30° bank at 150kts gives you the radius of about ⅔nm, which
technically allows for flying downwind as close as 1⅓nm from the runway centerline (adjust for deviations from the standard conditions and wind).