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

Minimal logic does not assume any falsity $bot$ or negation $neg$, so the above mentioned laws can (apart from Peirce’s) not be stated as usual. However, if we fix some propositional variable $F$, we can use it to define a kind of negation by $dotneg A := A rightarrow F$. We can then define
begin{align}
mathsf{LEM} &:= forall A. ~vdash_m A ~lor~ dotneg A
\ mathsf{DN} & := forall A. ~vdash_m dotnegdotneg A rightarrow A
\ mathsf{CP} & := forall A~B. ~vdash_m (dotneg B rightarrow dotneg A) rightarrow (A rightarrow B)
\ mathsf{Peirce} & := forall A ~B. ~vdash_m ((A rightarrow B) rightarrow A)rightarrow A
end{align}

where $A, B$ are propositions$^{(ast)}$ and $vdash_m$ stands for derivability in minimal logic. In intuitionistic logic (taking $F = bot$ and $vdash_i$ instead) they can all be shown to be equivalent.

In minimal logic, I succeeded in proving:
$$
mathsf{DN} leftrightarrow mathsf{CP} ~~~,~~~
mathsf{CP} rightarrow mathsf{Peirce} ~~~,~~~
mathsf{Peirce} rightarrow mathsf{LEM}
$$
The intuitionistic proofs I did for the other implications all needed the explosion principle and, at least to me, there seems to be no way of avoiding this. I don’t know much about the semantics of minimal logic, so my question comes down to:

Can the other implications be shown or is there some semantics showing the impossibility?

I did the proofs in part on paper and checked all of them in Coq by formalizing the deduction system for propositional minimal logic. (There is also MINLOG, but I have not worked with it so far)

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$(ast)$ The quantification here is not supposed to be internal to the logic. I am only considering propositional minimal logic here. So for example, $mathsf{LEM} rightarrow mathsf{DN}$ should be understood as "adding every instance of $A lor dotneg A$ as an axiom, I can derive $dotneg dotneg B rightarrow B$ for every proposition $B$".

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Update (5. April 2021): Today I found this paper

Classifying Material Implications over Minimal Logic (Hannes Diener and Maarten McKubre-Jordens)

Which pretty much sums up everything I wanted to know and more.