Times Full Metal Jacket Got History All Wrong

In "Full Metal Jacket", there's a scene towards the end of basic when they're singing happy birthday to Jesus. This is obviously a reference to Christmas. Shortly after, Joker graduates and is sent off the Vietnam as a reporter. When he's seen next his hair has grown out yet he still seems a bit new. People regularly comment that he hasn't seen any action.

Even more, Joker is talking about the Tet Ceasefire, and is present for the Tet Offensive. This timeline is all confusing. The Tet Offensive occurred in late January, 1968. So either Joker grew hair and was somewhat established with "Stars and Stripes" in less than a month or he was woefully under-experienced for his time in country.

"Full Metal Jacket" the movie is based on Gustav Hasford's semi-autobiographical book, "The Short-Timers." That term means somebody with a short time left in his deployment. This would imply perhaps that Joker was coming up on his 13th month, which would maybe make sense except that the idea he'd get sent into field during this big push is perhaps a bit unbelievable, and the idea that he'd go to fight in the Battle of Hue during his last month is certainly incredulous.