Keep all of your papers- especially the ones where you changed DL address.- and be prepared to bring them to court. Hiring a traffic ticket attorney might be the easiest way to deal with this. You will not have to appear as an attorney can appear for you. Which Court? Give me a call if you have any questions.
This sounds like a fairly normal and reasonable mixup. You thought that the LA Courts and DMV would be on top of everything? That will be the day.
I advise you to meet with an experienced traffic attorney. You started off owing $25 and now they want over $1,000. With a good attorney, you should be able to keep the final number much closer to the $25 than the $1,000. And, you can keep it off your record.