[geek hat]
Well now, this has got me to thinking - most of the specs line up: wingspan, length, and wing area are all the same.
However, height and empty weight are off by 11.5" and approx 12,000lbs respectively. This might indicate that

is referring to a variant of the Privateer.
Now here's something funny: the height in the lyrics (29' 1.5") is closer to the (P4Y-2) Privateer's 29' 2" than the PBY-4. The empty weights are also closer - lyrics, 39,400lbs, P4Y-2, 36,950lbs.
Given that

is something of a wordsmith, it could be argued that the P4Y-2 is the model he's referring to - the number 4 is often used in place of the letter A on license plates and things. If this is the case in this instance, what we have is a song called Pay To Privateer, literally "Pay up, suckers - I'm a free agent now."
[/geek hat]