If you can talk to a lawyer please do. It may be worth the potential insurance hike.
If not, here's my two cents worth. In my experience, no points means no foul. Given this, your record is clean. (If I understand you.) Check the laws on the placement of stopsigns. If they have to be visible, (and I'm sure they do) you have probably have a good case for getting that one dropped. You might show the pictures to the DA, maybe he can help. One possible snag. Is it a four way stop? If so can you see the other stop signs? If so you're ok. You can argue that it might have been a 3 way stop with your way clear. If you can't see ANY stop signs pointing any direction you're dead, because here, at least, you treat an uncontrolled intersection as a four way stop.
This leaves the one in Orange county. If you can do the school thing go for it. Worst case scenario, have your insurance agent check your record just before everything hits. If they're like my insurance company, they won't check again until time to renew. The hike may at least be delayed. Also, some insurance companies let you slide on one ticket. I hope it works out for you.
One other possibility. How much time do you have for your court date? How long is traffic school? It's possible you can get a later court date for one while doing the school for the other. Once that's done and the ticket is dropped you can take care of the other one.