Tom, I am workiing extensively with Chapter K and here's what latest edition say's (aside from what you've already mentioned):
K328.2.1 Qualification Requirements.
(e) Mechanical testing is required for all performance qualification tests. (Agreeing with Al)
(f) Qualification on pipe or tubing shall also qualify for plate, but qualification on plate does not qualify for pipe or tubing. (You already mentioned)
K328.2.3 Performance Qualification by Others. Welding performance qualification by others is not permitted.
K328.2.4 Qualification Records. Paragraph 328.2.4 applies.
328.2.4 Qualification Records. The employer shall maintain a self-certified record, available to the owner (and the owner’s agent) and the Inspector, of the procedures used and the welders and welding operators employed, showing the date and results of procedure and performance qualifications, and the identification symbol assigned to each welder and welding operator.
I believe where ASME IX permits P1 to qualify for P1 - P11, etc., these rules still apply, I see nothing in Chapter K to change them.