In OTL :
ITTL
Impressed by the expand of Western power in Asia and doubtful about the real aims of Japan, Gojong of the Korean Empire decides to contact Karl Ivanovich Weber, the Russia's first consul general to Korea (who IOTL was a personal friend) in order to find a solution against the Donghak Peasant Revolution of 1894. We are the 15th February 1894 (battle of Jeongeup).
Ivanovich Weber explains him that Russia is ready to help his country in exchange of the rights to exploit natural ressources and to use a few ports. One modern Korea is seen by the russian strategists has a good buffer against the Japanese expansion. It could also provide many ports and a control on the Korean Straits. Free navigation is necessary for developpement of eastern Russia. Russia can't let Japan control those straits.
Ivanovich Weber also tells him, that without any ally, Korea would soon be conquered by the quickly industrializing Japan. The only possibility to save Korean sovereignity was to accept one limited protectorate. Balancing the various foreign barbarians wasn't the best method to survive in the new world order. During the night, Ivanovich Weber teaches the young King about the European colonization process and about the real bad position of Korea in the world.
Gojong is shocked by such informations and decides , after months of deep reflexion and numerous discussions with members of the Court, to speak about the "protectorate" possibility to his spouse. He meets her in March and explains her that this system was similar to the symbolic tribute that Korea continued to pay to the Middle Kingdom. The Russians was he told, would just ask to minor economic and trade concessions, in exchange a small and light populated country like Korea would become able to resist to the gigantic China and to win a new battle of Myeongnyang against the modern Japan.
His spouse is astonished to listen to such political maturity coming from her usually weak husband. She asks him, where he found such valuable informations about the world. Informations which totally contradict the informations she gets from her officials. Gojong immediately introduces her to Ivanovich Weber who was waiting in another room of the palace. The man explains her that Japan has expansion plans projects which include Korea. He even informs her that the Japanese could decide to assasinate her, painting one very negative image of the Japanese leadership. It's a bluff, but it works.
Queen Min calls her court and diplomatically informs the Japanese and the Chinese about the arrival of a small number russian advisors into Korea. Weber was also able to persuade her to appoint a new cabinet consisting of a "pro-Russian faction" led by Yi Wan-yong, Yi Boem-jin and Yi Yun-yong (as in OTL). In May 1894 (1896 in OTL), Weber signs the Kormura-Waeber Memorandum with his Japanese counterpart Komura Jotaru, granting Russia the right to station troops and ships in the Korean peninsula, and requiring the Japanese to recognise the new cabinet (as in OTL). Russia will also acquire mining and forestry concessions in (the) North (of) Korea

as in OTL.
A second memorandum is signed with the Chinese envoy whose I forgot the name.
The main difference in TTL treaties is that Russia will not only send a huge number of troops, but also many civilians who will help to developp the country and to link it to the Trans-Siberian railways. Russian engineers, teachers and university professors will help to turn the Kingdom of Korea into one "Meiji Korea". Korean troops will participate to the international force sent to quell the Boxer Rebellion. This participation will ensure the entrance of Korea among the concert of civilized nations (and into the SDN later).
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Before the Russo-Japanese War, the Russian navy and the Russian troops firmly implanted themselves into Korea. The Korean military will also be modernized and ready to fight any future military aggressions from Japan or China. The Russo-Japanese War began in 1905. The Japanese decision to avoid the Korea theater took the Russian defensive plan by surprise. This plan was based on one massive Japanese attack on Korea.
The Japanese surprise landing between Vladivostock and the Korean Peninsula bypassed the Korean Peninsula. The consecutive Pyrrhic Japanese victory of the Yalu River pushed General Aleksey Nikolaevich Kuropatkin, in charge of the Far East, to keep his russian and korean troops inside the Peninsula for the duration of the war. The lack of those potential reinforcements turned most of the next battles into Russian defeats. The Russian troops stationned in Korea could have been able to send reinforcements to Vladivostock or Port-Arthur.
Even if the presence of Korean ports helped the Russian Navy to save some of her military and civilian ships, it couldn't avoid the surprise attack of Port Arthur and the disastrous battles of the Yellow Sea and ill-fated battle of Tsushima.
In accordance with the treaty of Porstmouth, both Japan and Russia agreed to evacuate Mandchuria and split its sovereignty between China and Korea, but Japan leased the Liaodong Peninsula (containing Port Arthur and and Talien), and got the right to use the Russian rail system in southern Manchuria with access to strategic resources. Japan also received the southern half of the Island of Sakhalin from Russia. The treaty also cancelled the Russian protectorate on Korea.
The British impressed by the "Bushido spirit" and by modernity of the Japanese forces, decided to renew the Anglo-Japanese Alliance. This renewal can easily be explained as a British tentative to counter the increasing weight of the Russo-Korean Alliance in the area. The necessity to block the expanding Russian sphere of influence in Eastern Asia was capital to protect the colonies of India and the Middle East, according to the geopolitical theory of Mackinder (OTL English vision).
--> Mackinder, H.J. "The geographical pivot of history". The Geographical Journal, 1904, 23, pp. 421–37.
Many historians also consider that this alliance was a product of the European racist Zeitgeist : The fear of the Eurasian peril. The idea of the new Eurasian hordes, consisting of the fearless Japanese, the numerous Chinese, the born for war Mongols, all commanded by the industrious Koreans and the treachous Russians was popularized by a few books and seemed to have been interiorized among the Western European elites. The British-Japanese Alliance was a mean to divide those potential hordes : Divide ut regnes.
During WWI, Korea fought alongside in the Entente and helped to raid the german port of Tsingtao, alongside the Japanese troops. After the Soviet Revolution, many white Russians fled to Korean administrated Mandchuria and to Korea. The Russian minority is still nowadays, the third minority of the Korean Republic, only outnumbered than the Chinese and the Mandchu minorities. Russian is one of the numerous minority languages recognized in the country.
The Korean political situation after WWI was grim. The Korean soviet party established by Soviet advisors, the Royal Party and the Korean Republican Party had been unable to find any agreements during two decades since the end of the war. A political tremor occured when the KSP and the KRP decided to launch a common referendum in 1929 to abolish the monarchy. The King prefered to abdicate. This sudden abdication plunged the country into chaos which almost turned into a civil war. One solution was finally drawned. The country would a parliamentary Republic and the King would stay the representative of the Korean nation.
The Mandchurian plebiscite united the de-facto Korean administrated Mandchuria with Korea into one dual Confederation in 1935. The interbellum period (1918-1944) was difficult for Korea without its russian traditional protector and ally. The country, fearing a japanese hegemony, quickly modernized its military forces and economy with the help of Germany and Soviet Union. Korea even chose to kowtow Japan and sent many Korean students in the country to learn the best of the Japanese universities. Many Korea officiers were also sent into Japanese military academies. The trade of minerals with Japan would not stop until 1944.
The Interbellum period is particularly long as Korea is basically in the same situation as Switzerland. A neutral country with good armed forces, able to provide goods to the belligerents. Korea also chose to have friendly relations with Japan, playing the role of one sycophant.
The begining of WWII wasn't a surprise for the neutral Korea which became on armored turtle. In mid-1943, Japanese tried to launch a sneaky attack from the South. After bloody delaying battles, the Korean loyalist troops were pushed as far as the 38th parallel north, saving the industries which were evacuated further in the north. The attack on Korea was finally repelled with the combined help of Nationalist China's and Soviet troops in 1944. Korean troops were among the first ones landing on Japanese Islands in 1947 and in Taiwan in 1948. Korean troops fought again on chinese soil from 1949 to 1990, helping to defeat the rebellious communist forces, called Maoists.
The Korea economic miracle is still famous in history. The 1952 decision to link the recovering Japanese economy and the developping chinese economy to the still prosperous korean market was a move of genius. The East Asian Economic Community (EAEC) which nowadays also include Indochina, Thailand, Malaysia, Philippines, Brunei, Indonesia and the Free City of Singapore was born. The economic and military presence of Korea helped to stabilize the area during the Cold War, even if military interventions were still necessary (Chinese Maoists, Indochina war, Indonesian genocide, Red Tibet crisis).
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