One of the ways I envision tunneling is the pole vaulter. At no time is the entire mass above the threshold; at no time is the center of mass above the threshold; and yet, the entire mass itself goes over the threshold. It is a pretty good illustration.
To extend the analogy, focusing on the center of mass and saying that it HAS to go above the threshold due to conservation of mass equations is simply wrongheaded. Focusing on conservation of energy on similarly micro-focused aspects of the overall energy system is also wrongheaded.
You haven’t answered my question, which is what isn’t conserved in tunneling? QM prevents us from talking about how transitions happen, only what the initial and final states are. If something isn’t conserved, I don’t know what it is, but the apparent physical impossibility of tunneling, in and of itself, isn’t a violation of conservation.