Okay, so, idea:
During the Siberian Ice March, Kolchak and Semyonov die of frostbite or something, and General Vladimir Kappel - young, charismatic, and beloved by his troops - survives. Kappel manages to hold together the ungainly coalition of surviving Whites, Czech, Turkish, and Italian soldiers, and American and Japanese expeditionary forces enough to destroy the Soviet backed government at Chita. A rough troika of Kappel, the Czech Legion chief of staff and religious maniac Mikhail Diteriks, and Admiral Georgy Stark ran a surviving rump state, which used a policy of religious nationalism, fervent anti-communism, and land reform to woo the locals - along with convincing some of the Czech, Turkish, and Italians to stay as settlers. The land reform program was enough to stay some of the terror campaigns perpetuated OTL by the Japanese and Americans, and - after a defeat by Admiral Stark's squadron and some retroceded Japanese warships of an attempted Red landing near Vladivostok - American encouragement of recognition of the White breakaway state by the Soviet Union succeeds.
By the late 1930s, the Russian Far Eastern State is a surviving White Russian polity encompassing roughly from Chita to Vladivostok, a little rump buffer state backed by (depending on the day of the week) the Americans or the Japanese. Nominally, an American style government and Tsar Nicholas III (formerly the Grand Duke Nicholas) rule; in reality the military troika has no incentive to give up power.