ICN - PEK - PKX - HND

Yes, you are correct. Your itinerary:

Seoul - Beijing - Tokyo

Is definitely and undeniably eligible for 144 hour visa free transit in wider Beijing area and you do not need any kind of visa. Also, it is perfectly allowed to use separate airports and separate tickets as long as your itinerary is eligible and your itinerary, if you have mentioned all the stops within it, is eligible. It is important to know that the first thing you will do upon landing in Beijing is to approach 24/144 hour visa free transit counter where you will apply for a temporary entry permit by presenting your flight tickets. After a permit is granted, you will proceed toward immigration. This application is free of charge. Have a nice journey.