If the meeting is being cloud recorded, it will only record the main room, regardless of what room the meeting host is in. If local recording is being used, it will record the room the participant who is recording is in. Multiple participants can record locally.
I have a single-user account (although I could temporarily increase the capacity if needed). Can I make three other people co-hosts and have them each record their breakout room locally?
It is true that cloud recordings cannot be initiated from within a breakout room, only local recordings can be done from within breakout rooms.
As for the co-hosts and recording locally, you don't need to increase your account or capacity, as you can just allow each of them to record in the meeting, move them into their breakout room, and they can begin to record. Just make sure they are each joined through the desktop client, as they cannot locally record from the web client or mobile app.
Hope that helps and please make sure to mark the solution as accepted if this information is what you needed.