The relevant check box is the "I am one of these passengers" box. If checked, the passenger name is prepopulated with the Skymiles member name and cannot be changed. If that box is left unchecked, you get general availability, and can enter the passenger name on a later screen.
I feel so very lame for not seeing it but where is this box? I started at the beginning on the page where you select roundtrip vs one way vs multicity, the origin/destination and flight dates - checked the box that said "I am flexible, show me more dates" and went all the way through really slowly. I know it has to be somewhere on one of the first screens so that the date search knows to present the appropriate flight options for non-Medallion pax - by the time I get to the message that the Medallion pax name cannot be changed, that's logically way too late for it to be appearing.
I understand now, I can definitely book award flights using these other two accounts as long as I can uncheck this box. I cannot find, please help . . . thanks, and sorry !