For those who are interested I present my itinerary for Korea, that included all WHS (several components if available) and seven TWHS.
Day 1: Arrival on Sunday 11am. Train to city center, metro to hotel (close to Jongmyo Shrine), walk to Changdeokgung, visit palace (including garden), walk to Jongmyo and visit, metro and walk to Jeongneung cluster and visit
Day 2: metro and train to Suwon, visit Hwaseong (complete wall loop, palace and museum), train to Seoul, walk to Gyeongbokgung (not WHS) with stop at a town wall gate, walk to city wall, walk back to old town.
Day 3: taxi and flight to Jeju. From airport all transport with rental car. Drive to Hallasan NP, hike to Mt Hallasan, drive to Geomunoreum with stop at Sangumburi crater (not WHS), visit Geomunoreum visitor center and reserve tour for next day, drive to Seongsan Ilchulbong and climb crater, drive to hotel
Day 4: Drive to Geomunoreum and tour, drive to Manjanggul cave and visit, drive to airport, flight to Seoul, rental car to hotel
Day 5: drive to Namhansanseong, walk 50% of wall and visit palace, drive to Heolleung tombs and visit, drive to Oeam village and visit, drive to Magoska Sansa temple and visit, drive to Gongju, visit Gongsanseong fortress
Day 6: Visit Songsan-ri tombs, drive to Buyeo and visit Baekje components, drive to Donam Seowon and visit, drive to Iksan and visit Mireuksa and Wanggung-ri, drive to Gochang and visit dolmen site, drive to Gochang tidal flats for sun down, drive to hotel in Naju
Day 7: drive to Unjusa temple and visit, drive to Hwasun domen site and visit, drive to Seonamsa and visit, drive to Naganseupseong and visit, drive to Suncheon tidal flats and visit, drive to Namgye Seowon and visit, drive to hotel in Hamyang
Day 8: drive to Haeinsa and visit, drive to Goryeong tumuli and visit, drive to Gyeongju, visit Seokguram and Bulguksa, visit Gyeongju monuments, drive to Yangdong village and visit, drive back to Gyeongju and visit by night
Day 9: drive to Hahoe village and visit, drive to Byeongsan Seowon and visit, drive to Sosu Seowon and visit, drive to Buseoksa temple and visit, drive to Ondal fortress and visit, drive back to Seoul and return car
Day 10: Short stroll in Seoul and flight back home
A few remarks: the trip involved a lot of driving and 30'000-50'000 steps per day. You have to work around Monday closures in Seoul region. I usually skip lunch and get up early to maximize time. Jeju could have been done in one day, as there are tons of flights from early to late. I went in February and didn't have much traffic. I heard in high season you need more patience on the streets. Ordering food in the south is not fun if you don't speak Korean.