Here ya go:
[snip] ...carbonized “fava” beans from a mining installation between the villages of Akrotiri and Meghalochori. The latter sample was found in a large jug buried beneath a layer of pumice at the edge of the preciptous side of the caldera. It dated to 1420 - 1400 ± 60 B.C. [end]
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.