Just been able to check FARs (it has been a while since I used my FAA license). FAR 61-51 covers this:
Sec. 61.51
Pilot logbooks.
(e) Logging pilot-in-command flight time.
(1) A sport, recreational, private, or commercial pilot may log pilot-in-command time only for that flight time during which that person—
(i) Is the sole manipulator of the controls of an aircraft for which the pilot is rated or has privileges;
Note the requirement is to be rated or to have priveleges, NOT to be current.
and significantly:
(3) An authorized instructor may log as pilot-in-command time all flight time while acting as an authorized instructor.
So I stand by my original premise that in these circumstances the pilot regaining currency, being the sole manipulator of the controls of an aircraft for which he/she is rated or has privileges, is entitled to log P1. From the above, the instructor will also log P1, so the total P1 time will indeed exceed the sector time.
Similarly, during a routine proficiency check (FAR 61.58), the flying pilot will normally be current to begin with, so is definitely entitled to claim P1 as the sole manipulator of the controls of the aircraft. Instructor can also claim P1.
This is FAR remember, not JAR. Anyone disagree?