The studies you cited were conducted in 1967 and 1977. By today's standards the accuracy or precision of the test methods used was primative. (What kind of computer did you use in 1977? I thought so.) Aside from significant improvements in the supporting analytical equipment there have been improvements in methodology. A breakthrough has emerged from recent research into the fluctuation patterns of the original 14C content of the Earth’s atmosphere over the past 50,000 years.
Science is not relying on radiocarbon dating and tree ring analysis alone. Since the studies you cited were conducted there have been dramatic developments in a range of other specialist dating methods. Some of these are more suited to dating rocks, ash and ejecta adjacent to your "fava" beans. Methods include potassium-argon dating, uranium series dating, fission-track dating, amino acid racemization, and archaeomagnetic dating. Of far more value with prehistoric archaeological remains are thermoluminescence (TL), optical stimulation luminescence dating (OSL), and obsidian hydration. The last of these is restricted to obsidian finds associated with volcanic activity, which form a surface hydration layer when exposed to air, the thickness of this layer corresponding with the length of exposure.
The RC dates were all conducted by the same lab. The fava beans (or as you put it “the ‘fava’ beans”, for no apparent reason) are a better example, because they had an origin obviously closer to the date of burial than, say, a tree. The main problem with RC dates on Thera has been that the soil is poor in C14 due to past volcanism (imagine that), such that stuff grown today will test hundreds of years too old.
All the rest of your reply is irrelevant to the dating of the *very small ash layer* that buried the town — supposedly during a super-eruption. And that’s what I thought we were discussing, apparently you were not. Goodbye.