Actually Plan to invade Liaodong in 1388 was last chance for Korea to manage control of Liaodong. However there was one major "IF". In 1388, Ming launched massive military campaign against Northern Yuan.with the troops of around 150,000. IMO, Yi Seong-gye can invade the Liaodong, but whether Koreans could retain its control rests on Northern Yuan's success against Ming Dynasty.
Lets say Yi Seong-gye invaded Liaodong. At the same time Northern Yuan with some big luck manage to defeat Ming forces. Now Northern Yuan, Goryeo establishes alliance against Ming Dynasty. I think Northern Yuan-Goryeo alliance is enough to withstand until death of Hongwu Emperor.
Now what happens next? Will Yi Seong-gye establish Joseon Dynasty and become King?
Lets assume Joseon is founded by Yi Seong-gye and Jeong Do-jeon at the same time as Hongwu Emperor's death. Then they strike deal with Zhu Di and help him become Emperor. Joseon will be allied with Ming ( or even could pretend as a tributary state as long as they accept enlarged Joseon). This cements claim of Liaodong and with couple of generation Liaodong is populated by Koreans ensuring long term control of Liaodong peninsula.
What the effect of Joseon with the Liaodong territory?
1. This will boost arable land thus more population and more taxes, more wealth. It will greatly increase Joseon's power.
2. OTL Joseon constantly beat Jurchens. ITTL, Joseon will even more suppress Jurchen and invade them. Maybe Joseon and Mongols could partition Jurchens. So Jurchens/Manchus ITTL will be extremely weakened thus potentially butterflying Qing Dynasty.
3. Wild card would be Imjin War. How more powerful Joseon will fare against Japanese invasion ? If Imjin War severely weakens Joseon, would Manchu's use the opportunity and rise? But the process of founding Qing will be long and painful process with weakened Jurchens.
3. Without invasion of Qing Dynasty, Fall of Ming Dynasty could last longer. How long Warlord Era will last? At least by late 1680's there will be established another United Chinese Dynasty.
4. Without Qing Dynasty, Mongols will be united under Dzungars.
5. Without Qing Dynasty how far expand Russian Empire in Manchuria? OTL Russians tried to establish border at Sungari river. So they could take control of Outer Manchuria during Peter the Great reign.