1. Do you really mean JFK or do you mean NYC (which includes EWR & LGA)?
2. Both UA & US are *A and fly various routes between NYC & LAX. UA flies non-stop xJFK & EWR.
3. UA offers 3-class service on JFK-LAX. It's Business Class is designated "C" not "J".
4. All other services on UA and US are 2-class and are generally designated as "Y" or "F", although UA has some 2-class Business First service.
My strong recommendation is to toy with the *A booking tool to pull up a listing of NYC-LAX (or JFK-LAX is you are stuck with a single specific airport) and then work to locate the best deal for your miles based on your specific travel needs.