Agreed.
My preferred solution would be if there was a notification that appeared on the screen when your partner entered conversation. Clicking the notification or an assigned hot key would open the dialog in a screen that works mostly the same as the current journal, only you'd also get your co-op dialog choices in that same screen instead of getting yanked to another one.
You could have "auto-open conversation" as an toggle option for those that want to make sure they never miss one.