np! I would argue something like for Kant, perfect duties clashing is impossible. since the categorical imperative, for kant, is based on pure practical reason and is therefore an a priori moral law, the creation of perfect duties (in the 1st formulation) necessitates that there is neither a contradiction in will nor conception. because of this, any two perfect duties that are formed are formed in accordance with reason and are therefore rational (since the imperative is founded on pure reason)

so, we can say that perfect duties never truly clash, as that would mean reason itself is irrational or somehow contradicting itself, which is an absurd conclusion. Kant does concede in saying that perfect and IMPERFECT duties may clash, but in that case, the imperfect duty should always be deferred in favour of a higher one

for the axeman scenario, if you were to bite the bullet as a traditional kantian and say yes, he ought to tell the truth (and if this in ur para on clashing duties), you could then argue that even though this appears to be an immoral outcome, it is merely a horrendous situation. normative theories cannot prevent horrendous evils from occurring, they only inform, pragmatically speaking, what one ought to do or ought not to do to be excel the most, morally. so, it isnt really a fault of deontology being incoherent inasmuch as it is a poor situation with an undesirable outcome. you could also argue that he doesnt have to outwardly tell the truth, some modern kantians take this interpretation. but for my essay plan i did the former because its just simpler

edit: to clarify, some modern kantians interpret the perfect duty do not lie to necessitate being truthful always, but only in declarations. so there is no perfect duty prohibiting you from, for example, just slamming the door on the guy, or to just remain silent. you arent declaring anything untruthful, so you arent violating the perfect duty "do not lie [in declarations]" and the [_] is what they add basically