When scheduling a deployment, is there a way to specify values for parameters? So far it looks like setting an override value for a parameter sets it for all flow runs (not just for the scheduled flow runs.)

Like a default?

Each deployment of a flow can only have one schedule and one set of parameter overrides. If you're looking to use something other than the param values that deployment was created with, you can always change them when you do an ad-hoc run. If you want a way to always run that flow with only its defaults, create another deployment for it that doesn't specify parameter overrides or a schedule.