I am by no means an expert, but my understanding is that saxophone manufacturing got a lot better by the 80s, and lots of the older horns are known for shifting more and more out of tune at the ends of their range. Players often use tuning apps or just their ear to compensate by lipping it up or dropping the jaw a bit to make individual notes sharper or flatter. I grew up using a vintage horn and when my son’s saxophone teacher mentioned that, I realised that is exactly what I had always been doing without thinking about it.

If you are finding that you are consistently flat or sharp across the entire range, that may be something you can correct with practice. If you haven’t been playing for the whole 10 or 11 months since you set it up, it may just be taking you time to adjust to the changes. My son was advised to play for 2 to 3 months before taking any big swings at his, and sure enough it became easier and easier to get it into tune without pushing the mouthpiece to the end of the cork. And some horns need more frequent adjustments than others no matter what. Best of luck with figuring things out!