I have a rule of thumb: Multiply p by 10. In other words, p = 0.05 is as good as a coin toss. This is consistent with the so called replication crisis.

In my view, understanding p-values won't help. Feeding data into a formula that produces a p-value doesn't account for things that can go wrong with experiments: Uncontrolled experimental conditions, biased sampling, hidden correlations, and simply non-ergodic systems. It is possible that some systems can't be controlled to the point where it's reasonable to start looking for real effects.

I suspect that if the results were any good, the precise interpretation of the p-value wouldn't matter. Physics has lived without an agreed-upon interpretation of quantum theory for a century.