You’re correct, but the H-40 also got its designation before 1962 as well…
So I still see a a discrepancy.

The H-2 and H-3s initally had designations under the old Navy system, so they had to have new numbers post 16 Sept 1962. But there was no need for the Huey to change from the H-40 because, like the C-141, it had a USAF-style designation.

But the change from XH-40/YH-40 (assigned 1955 by the US Army, 3 and 6 built respectively) to HU-1A occurred in March 1960 when the production orders were placed.

This was 2½ years before the system change, so it was an internal US Army decision… perhaps some period publication gives a reason.