Radioactive decay

Let's consider the Mathematics of radioactive decay (Wikipedia). Given a sample of a particular radioisotope, the number of decay events $-dN$ expected to occur in a small interval of time $dt$ is proportional to the number of atoms present $N$, that is: $$ -\frac{dN}{dt} = \lambda\,N $$ Where $\lambda$ is the decay constant of the particular radionuclide. The solution to this first-order differential equation is: $$ N(t) = N_0\,e^{-{\lambda}t} = N_0\,e^{-t/ \tau} $$ Where $N_0$ is the value of $N$ at time $t=0$.
A commonly used parameter is the half-life. Given a sample of a particular radionuclide, the half-life is the time taken for half the radionuclide's atoms to decay. For the case of one-decay nuclear reactions the half-life is related to the decay constant as follows: set $N = N_0/2$ and $t = t_{1/2}$ to obtain: $$ t_{1/2} = \frac{\ln(2)}{\lambda} = \tau\ln(2) $$ An argumentation for decreasing radioactive decay is found in the binding energy of nuclei. We have seen that all energy in the cosmos is increasing with time. Therefore all energy is decreasing if we look backwards in time. Especially the binding energy that holds a nucleus together must have been weaker in the past. This means that young atoms are more likely to decay than old atoms. The other way around: decay speed has been decreasing, if we follow the time path from past to future. But an argument against this may be found in Fermi's golden rule (Wikipedia). If such is the underlying mechanism, then it should rather be assumed that radioactive decay is actually the most stable clock imaginable in nature, which is independent of almost anything.

If it may be assumed indeed that the decay half time $\,\tau\ln(2)\,$ is independent of atomic processes - like those governing the inner workings of an atomic clock - then we have an additional argument. Suppose that the invariant decay process is compared with the timing of living species, that is: time is measured with atomic clocks. Then we can apply once more the INVERSE rule for measurements. Seconds of our clocks are proportional to $1/m_e$ and hence decreasing as time proceeds. Therefore the decay seconds measured are increasing, meaning that the speed measured is decreasing. With other words: the speed of radioactive decay appears to be slowing down and has been "faster" in the past.
Radioactive decay may be measured with an orbital clock instead of an atomic clock - as is done for example when comparing radiometric data with seasonal growth rings in trees. If such is the case, then radioactive decay speed is expected to be even more decreasing with time, namely $\sim 1/m_e^2$ instead of $\sim 1/m_e$ .

One of the major objections agains a more intense radioactivity in the past is put forward by Joe Meert: Were Adam and Eve Toast?. With the above theory, it is clear that this argument does not hold water anymore, because radioactive clocks most probably have been invariable through time. But when age is measured with other "clocks of evolution", that is (chemical) atomic clocks or (growth rings) orbital clocks, then nuclear clocks appear to be ticking (much) faster in the past.

Disclaimer: this field of interest is definitely not my expertise. Therefore I've asked some questions about the inner workings of $\beta$ decay to a supposed expert in the field, Gerald Aardsma, without obtaining a satisfactory answer, though:

My question is whether two formulas about radioactive decay in Setterfield's book are correct or not.
I'm especially interested in the dependence on (m), some mass of a sub-atomic particle (don't know which one).
My personal bias is that radioactive decay is independent of most things and I cannot imagine that mass plays
a role. But my knowledge on the subject is very limited.