I'm not familiar with the area and I couldn't figure this out just from your description, can you point at the spot on Google Maps where you crossed the double yellow? Is it West River Dr. / MLK Jr. Dr. going south?

It's just a traffic court, you don't need a lawyer if you can make a coherent speech to the judge.

I took a look in street view and I see a "speed limit: 35" sign going south about 1000' past the Roosevelt Expressway bridge. In any event, the cop would have trouble proving that you were speeding if she did not measure you with a radar. I'd ride through that area again and make note of any speed limit signs, and mention them to the judge.

I don't see what the 10 mph bike path restriction has to do with anything, since it sounds like you were not in a bike path.

"Reckless" part depends on what the cop meant by it, you can try to argue that you weren't being reckless.

"Crossing the double yellow" would be hardest to beat. There may or may not be an exception for crossing a double yellow under these circumstances. (I took a look at the PA vehicle code and I don't see one.) This is the only place where a lawyer could help, but it would not be worth to hire a lawyer just for this, since you'd probably pay more to the lawyer than the fine you're contesting.