Rows under counters/tables might be useful before your rings arrive:
https://www.youtube.com/watch?v=OYUxXMGVuuU

Once you have the rings, for the dips, if you haven't done them on rings before, be careful with your shoulders.
You can offload weight using your legs and it can also be helpful to strengthen your ring support (https://www.youtube.com/watch?v=kONbxg4kzkE)

I've experimented with bodyweight pretty extensively and might be able to help with other gaps in your routine. Hope this is helpful.