Excluded middle, double negation, contraposition and Peirce's law in minimal logic

$\mathsf{Peirce}$ is stronger than $\mathsf{LEM}$, but it happens to be interderivable with generalised excluded middle $(\mathsf{GEM})$ $$ \mathsf{GEM} := \forall A~B. ~\vdash_m A ~\lor~ (A \rightarrow B). $$

A weak form of Pierce's law is interderivable with $\mathsf{LEM}$ $$ \mathsf{WPierce} := \forall A. ~\vdash_m (\dot\neg A \rightarrow A) \rightarrow A. $$

None of these four principles are enough to derive $\mathsf{Explosion}$. These results, as well as ones that you mention in your question body, are listed as proposition 3 in Minimal Classical Logic and Control Operators by Zena M. Ariola and Hugo Herbelin

Using the results form the paper mentioned in the update, there is another way we can argue why $\mathsf{Peirce} \rightarrow \mathsf{Explosion}$ can not be possible.

Assume it holds, then it means we have a way of deducing $\forall A. \vdash_m F \rightarrow A$ from $\mathsf{Peirce}$. Since $F$ does not appear in $\mathsf{Peirce}$, this means we can use practically the same deduction to show $\forall A. \vdash_m B \rightarrow A$ for any propositional variable $B$, not only the particular choice $B = F$. So we get $$ \forall B~A. ~\vdash_m B \rightarrow A $$ This implies, that for any $X$ we have $\vdash_m (X \rightarrow X) \rightarrow X$ which in turn implies $\vdash_m X$. So we would have the highly problematic $\forall X. \vdash_m X$.