I should have said that the Type 99 was the standard Japanese service rifle in WWII, not that it was the most common. The Type 38 had been in production since 1906 and the Type 99 was only in service for 6 years at the most - late 1939 to August 1945, so we would expect that there would be more of the older rifle in use, even in combat zones.
But I can find nothing in any of my sources to indicate that Type 38 rifles remained in production throughout the war, or in Japan, beyond the introduction of the Type 99. The conversion of factories was done in reasonable time, made easier by the similarity of the two models. If Type 38 production continued even into 1943, there should be rifles showing signs of wartime manufacture; I have not seen any. AFAIK there are no "simplified", "modified" or "last ditch" Type 38's. All I have seen indicate normal peacetime production, and were of generally of good quality.