Since during the Joseon dynasty, and even during Sejong's time, Hangul wasn't used as the primary form of writing, I suggest using a mix of hanja and hangul instead.
Like in the far right column of this for example. With the hanja in large font and the corresponding hangul in a smaller font to the bottom right of each character.
Original: Korea during the Joseon Dynasty
Current: 조선 왕조 시대 한국
Suggestion: "朝鮮時代/조선시대" or "世宗大王時代의 朝鮮國/세종대왕시대의 조선국"
Meaning: "Joseon era" or "The country of Joseon during the era of Sejong the Great"
The term "한국" only refers to the Republic of Korea and didn't exist until after WWII.
Original: 1392 - 1897
Current: 천팔백구십칠 에 천삼백구십이 (You have this backwards here)
Suggestion: "千三百九十二年부터 千八百九十七年까지/천삼백구십이년부터 천팔백구십칠년까지"
Meaning: "From 1392 to 1897"
Though I think it would be best to just delete this portion since already using the word 時代/시대 makes it redundant.
Original: Korea
Current: 한국
Should be: 朝鮮國/조선국
And here's a list of all the hanja for other things on the map
黃海/황해
東海/동해
中國/중국
日本/일본
羅津/라진
鏡城/경성
咸興/함흥
義州/의주
平壤/평양
海州/해주
漢城/한성
江陵/강릉
淸州/청주
大邱/대구
光州/광주