I've reached a limit of mystification. Attempting to run an MPI application using MPI_Comm_spawn from a host is resulting in bizarre, inconsistent behaviour of ssh and ssh-askpass.
What I did is, I created an RSA keypair using ssh-keygen, copied the public keys into the ./ssh directories on the machines I'll be running MPI on, put them in the authorized_keys file, placed all the machines in the known_hosts file on the launcher host (which is starting MPI_Comm_spawn), then ran eval ssh-agent and added the id_rsa file to the agent on the launcher host.
You can verify that this part of the system is working because I can use ssh directly to access the worker machines that will be running the application.