Everything but the Tarim Basin thing could work, given Tibet does not have much with the area.
Have some ambitious upstart take control of Tibet and focus on claiming Qinghai and possibly Xinjiang Try and play off the Red and White Armies, getting British support and arms. They do a token effort against the RUssians, but focus on consolidating their hold, including some attempts at restoring the original Buddhist beliefs within the area. Make peace with the USSR and try and keep their new land. Either cause conflicts with Chiense Communists or get them to agree.
Focus more on cultural restoration, mainly in Qinghai. Also maintain postive relations with the British. Probably get involved with China, depending on who will give them the better deal or benefit in the long run. Granted, they might keep the Communists from entering and ensuring the Nationalists may be victorious. All about who gives them the better deal, though they'd have the West try and convince China to let Tibet keep their ancestral lands.
Xinjiang/Uyghurstan would not be as big a priority as Qinghai
Also, Tibet would try and get the British to give them Ladakh.
Basically help out the Allies in China and a Tibetian Empire ensuring they get a China who's leadership aligns to their interest (namely leaving them alone and possible alliances.) Beyond that, probably remain a cordial ally for the West. Focus on developing technology to their own ends, but otherwise remain fairly isolationist with a controlled tourism industry. Try and be on good terms with India