I’ve read a bit of the suggested New Zealand artillery history, including Chapter 8 on 144 Independent Battery, equipped with the 3.7-inch mountain howitzers. Interestingly, in the third paragraph of that chapter there is this statement: “...finally, in November , the guns arrived. Even then they had to be sent to ordnance for overhaul and there was only enough motor transport to move one troop at a time...Early in December the battery moved down to the vicinity of Lake Rerewhakaitu, near Rotorua [New Zealand], to carry out calibration of the guns.” One notes that also in November 1942, the Aussies were bringing their 3.7-inch mountain howitzers—the very ones oft described as “well worn”—ashore near Buna, Papua New Guinea.
Could it be that all or most of these pieces were from the eight such howitzers New Zealand had acquired sometime during the 1920s? Of course, in November 1942, the Aussies had three or four on the original wooden spoked wheel carriages, and the Kiwis needed eight to arm two troops of 144 Independent Battery. It does appear that such a number are arrayed on the beach at Nissan Island in February 1944, but having wheels with pneumatic tires. Further on in that chapter, there is nothing mentioned about those original howitzers needing overhaul either being modernized to high speed or replaced. The Kiwis spent a lot of time in garrison duty hither and yon, and got into the Solomons scrap pretty late in the game, so either upgrade or replacement of their ordnance could have readily happened.
But 3.7-inch mountain howitzers were certainly busy elsewhere. Here is one being manned by British gunners in the Arakan in the same month the Nissan Island photo was snapped.