In this paper the theory of canonical transformations associated with the relativistic dynamics of extended (i.e., finite-size) classical charged particles in the presence of electromagnetic radiation-reaction is addressed. As an application, the problem is posed of developing the corresponding Hamilton-Jacobi description which realizes the dynamical causal flow by means of the appropriate Hamilton principal function. The treatment is based on the Hamilton variational principle, which permits one to couch in an axiomatic framework the construction of the Hamilton-Jacobi theory for the electromagnetic radiation-reaction problem.