Welcome to posting on WIX, David. Your link to the State Library of Western Australia just may have solved the mystery of Waltzing Matilda's original name.
I blew up the photos you linked to, and found the "shadow" of ship number 54 on the right side of the fuselage (and after doing so, I see the evidence is also visible on the second photo James started this thread with). The tail has the same shadow where the "K" in a black square was stripped off before she went on tour. By going to this website;
http://www.rootsweb.ancestry.com/~ny330bg/b29sn.htm
it appears that she is 44-69774, K-54 of the 330th Bombardment Group, 459th Squadron. She had two names, the official "City of Paterson" and the "real" name, "Keohane's Kulprits".
Here are a couple of photos that support my theory, this first one is from the State Library:
Here is my blown-up shot of the tail, notice the remnants of the black square and K on the vertical, the lead ship stripe on the dorsal fin, and the 54 at the crew entry door:
Here is a shot of K-54 from the 330th Bombardment Group website--notice the placement and font of the numerals at the entry door again:
And a shot of the Keohane crew and their mount, again from the 330th BG (VH) site. Notice that the 330th BG "official" nose art is in the same exact position as the V-and-Australia logo on the first photo above:
And as a form of reference for the actual Square K markings on the tail, here is a shot of a sister ship, "City of Miami Beach":
I think the evidence we've got now pretty well ties down the identity of the airplane, but I had a bit of trouble with the 330th BG serial number listing. The webpage shows her as a B-29-60-BW but the serial listed is 42-69774, which is a P-63. Dash 60 B-29s were 1944 fiscal year production, and Baugher shows 44-69774 as a -60. There are several other aircraft on the 330th listings that have the same error.
Thanks again for the posting, David!
Scott