Yes go ahead and book a flight from STL to LA. Since it will not be an officially connected flight and likely on a budget carrier, I do suggest you plan to arrive in LA at least 4 hours before the flight.
LA is crowded and very slow for immigration and security, and budget airlines can be an hour late in taking off, so better to be safe, even if it means more waiting time in airports.
The reason your return flight is much shorter is because of prevailing winds of 100 kph. You will fly into a headwind when coming and be assisted by a tailwind when going home.