Good plan but this statement is not true sadly.
A PJ is a “sorta P” with some unique tonal options. It will never be a J, and the pickup placement of the P makes it quite different from a straight P.
I have a lot of PJs (mostly Aerodynes) and they are great because I’ve got lots of very different, specific pickups in them, but I am still often reaching for a straight P or J for tone or fit with a tune. FFIW
I don’t agree that a Sire is a cheaper Fender either. They are cheaper but I myself have not played one and thought “it’s a Fender”.