You're getting a lot of advice from some very experienced (and expert) airgunners.
After reading this and other threads, I see you are listening and working to get a solution.
And for disclosure, I'm a field target shooter myself, and had some similar head-banging concerns about my shooting and my equipment. One of the great things about my airgun experience was the idea for a product called Pelletgage that can easily check the head diameter of pellets. I have sold a lot of them to shooters worldwide, and have numerous reports from users who found and solved issues with their pellets. As Hector points out, they can vary. Most shooters seem to find a brand, weight, and type of pellet that works well, and stick with that. In my case, the JSB (or Air Arms) pellets are the go-to. H&N are popular, as well. But there are cases where a lot (or a tin) can have enough variance to be a problem, and that variance can produce the kind of hard-to-explain results you describe.
Here is a BLOG post by a very serious varmint hunter, Cliff Tharp. Cliff uses high power PCP rifles to shoot prairie dogs at long range. His equipment, skills, and experience in this type of shooting are up there with the very best. Early on, Cliff purchased a Pelletgage, and he wrote about what he found.
If you're shooting FT, ask to borrow a Pelletgage, and check that tin of FTT's. My suggestion is that the tin should have a mean size with a two sigma variance with +/- 0.01 mm limits. For a mean size of 4.52 mm (as an example), 95% would be found to have diameters of 4.51-4.53. Also, doing a sampling and finding the mean diameter of the pellets that shoot well in your gun lets you know which size to buy in future. If you sample 50 pcs from a tin of 500, no more than one should be more than 0.01 mm from the mean size. Note also, the mean size could be 0.02 mm or more from the nominal size you think you have!
You seem to have a capable rifle, and I will bet that if you keep plugging away, the problems will be solved. I switched to a PCP rifle, and it still took more than a year of shooting it, making adjustments, etc before I could compete in field target.
Here are some suggestions (some you already heard) based on my experience:
1) get that chronograph, and use it to see that you are getting a consistent velocity. If you don't have that, accuracy will be impossible.
2) avoid drinking any caffeine for hours before shooting.
3) a stable scope mount can be hard to achieve - make sure that your mounts are secure, but also that they don't impart any pressure on the scope tube. This amplifies the effect of temp changes. Even good mounts can have a latent torque or bending moment that shift the scope enough to matter. You might re-mount, and be careful to tighten carefully and evenly. In some cases, going to a quality one piece mount would help. Some people even lap the scopel