tell your agent you’re interested in contacting all owners about (mention some important matter) and for that you would like their names and email addresses to be sent to you (in no longer than say 3 days’ time). The agent cannot deny you that.
Are you sure? I don’t recall anything in the legislation that says the agent must forward owners anything. You are right about allowing inspection for a nominal fee. Take your phone and photograph or scan the lists to save you photocopying fees, if you want.