How do you stop phones from changing medpros in the middle of a call?

create a network region that only has one medpro assigned to it, and make sure the endpoint registers in a way that forces the endpiont to use that network region (using the change ip-network-map table).

Does enabling shuffling or disabling do anything to prevent this?

Disabling should help keep you anchored, but depending on what else is involved in the call, and what changes occur in call participants, Communication Manager can and will shift the call to the most efficient resource it can figure out. ... Generally speaking it tries to optimize resources, and then optimize bandwidth. Net result is as a call's topology changes, so might the resources involved. With shuffling enabled, a two party call that becomes a three party call will flip flop from direct media, to Communication Manager based media. With shuffling disabled, a call will remain on the medpro that was allocated for it, until something more efficient comes along (triggered by a change in the state of participants in the call (held, connected/disconnected).