"Th register is off about the same amount when the
blade is pulled back toward the mower."
That sentence says it all.
You CAN'T fix what ain't broke!
If the center of the knife sections passes the guard centerline by the same amount on the "in" and "out" stroke, all is well!
Typically, the stroke of the sickle drive is a bit more that the center-to-center distance on the guards, and it is NORMAL for the center of the knife sections to pass the guard centerline on the "in" AND "out" stroke.
(BTW, it is a SICKLE mower!)