I just lost a rather extensive reply. I really hate Windows. However, I will try to redo.
I looked at your pieces in your shop. Thank you for the pictures that are in focus. Some ideas --
I agree, you do not want to invest the time to solder all of those joins, especially in such intricate designs. So:
1. you might want to consider split rings instead of jump rings (however, they are quite difficult to work with)
2. you might want to consider using harder wire (the metals you are using do not work harden well)
3. you might want to consider making your own jump rings using the harder wire, I make my own rings in copper and sterling silver. I made a Byzantine weave copper bracelet, that took 50 feet of wire to make the jump rings, and have hard no problems with separation of the rings (none are soldered).
If you find that these things increase your time, I actually think your prices look a little low for the intricacy of your designs and in my mind the difficulty (time) that they take to make. As an exercise, take your price, subtract the cost of materials, then divide the remainder by the time that you actually took to make the piece. Are you even making minimum wage?
Check you rings, if you are manipulating them with your fingers, they are way too soft. You might be able to slightly increase the hardness with burnishing your rings in a steel shot tumbler.
Sorry for the rambling, I am also retired and it is late after having four of my grandsons staying here all day. I was totally pooped and fell asleep during wheel and jeopardy. If you have any specific questions, or inquiries, please feel free to contact me. I'll try to assist as well as I can.