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In this paper by Wu et al. https://www.fceia.unr.edu.ar/~mauro/pubs/haskell2019.pdf they show how to encode callcc using (first-order) algebraic effects.
@Lysxia Nicolas Wu is on Slack under the handle @zenzike
(I don't know the answer to your question :) )
good idea :)
if he responds could you copy the response here? thanks :)