Any chance you have access to other photos of the rear fuselage section before it was stripped? The FAH number was also carried on the extreme tail just under the horizontal stabilizer. That would at least tell us the identity of the aft section of the plane.
The 'Hollywood Wings' Corsairs were all disassembled into their major components and arranged in outdoor storage on a grassy side lot at the Long Beach Airport. The two men running the operation also had some warehouse space where they kept the smaller parts like cowlings, etc, as well the huge cache of spare parts also recovered from Honduras.
Another interested buyer who visited the site took some notes describing each major component still present during his visit, and 124493 was one of them. It's hard to judge from the single photo you have showing the center section, but what I can see of the plane does match his notes below...
Quote:
-5 Tail #608 (124493)
LH Door - missing
RH Door - strike
Tail wheel & strut missing
RH avionics door missing
Center Section F4U-5N #608 (124493)
Cockpit Fair No Rudder Pedals
No Windshield & Cowl
RH Fold OK, LH upper Air Duct OK
No Oil Coolers
LH Air Duct / Intercooler Rib Dam
LH Fold Minor Skin
RH Bomb Rack Bare
RH Strut Bare
No LH strut
Of the planes present at the site, 124493 was the only one who's bomb rack and strut configuration matched this description, thus I believe the center section John Mullen & your father recovered was in fact BuNo.124493. That would mean that the various components and identities must have gotten juggled a bit during restoration in Florida.
*note - This is complete presumption on my part, but looking through the lens of a mid-1980's mindset, the chain of logic might have gone something like this...
The fact that BuNo.122179 was the only airframe previously registered and flying could be the reason it's identity was used - possibly to minimize the paperwork and expedite the registration process for airworthy operation. Following that, the identity of BuNo.124493 might have proved helpful in smoothing the export process of the previously unidentified but externally complete airframe (123168) to New Zealand. That would leave the dead and burnt (at the time) remains of the real BuNo.122179 to be thrown into the dust bin with the otherwise undocumented and unsupported identity of BuNo.123168. That would be my best working theory on the matter anyway, all of which would need to be backed up with some further research.
Keep in mind that twenty plus years ago, bouncing around components and identities or partially dismantled non-flying aircraft was not seen as quite the insidious an act as most would consider it to be today. Most folks were simply looking to "keep 'em flying" back then, by whatever means...though it does wreak havoc on the bean counters like me.

_________________
Rob Mears
'Surviving Corsairs' Historian
robcmears@yahoo.comhttp://www.robmears.com