I have read two books about Greg Boyington and the Blacksheep. In each account, Maj. Boyington did not have a personal aircraft, whats more, none of the blacksheep did. In photo ops. he was photographed in a shiny new model F4U complete with japanese plane kill stickers on the side that was being photo'd.
Also, the Blacksheep were supplied with older modelled F4U's with the birdcage canopy and, newer models with the bubble canopy. They flew whatever plane was properly serviced and available. The original F4U1-a was outfitted with the birdcage canopy. As the pilots complained about the poor visibility of the planes, the manufacturers reps would report the complaints to the company and adjustments were made either in the field or with the next batch of planes shipped out to the frontline airfields.