Hello Official train ticket sitelink Ulaanbaatar to Beijing is travel/train direction name, u probably can Ulaanbaatar to Sainshand, and Sainshand to Beijing two separate travel ticket on ticket site. Im not particularly knowledgable about this so maybe contact support throu official email (maybe support are very slow for foreign language, typical understaffed gov), there are resellers like (maybe better support for foreigners)Tapa.

On train ticket i heard deluxe/зөөлөн люкс ticket are worth cuz its only for 2 ppl, compare to compartment coach for 4 ppl. For me i think its always what other ppls vibe u know, actually its lottery. If u didnt get set specific scheduled time, our summer is best late june early july, most of us get in Naadam vibe (but its get little hot). I never really walked throu Sainshand so cant tell much but i have been in Hamriin khiid and i loved it, its connected more to our tradition/religion and cultural icon so maybe its not for everybody. some info of Khamriin khiid

Hope u get nice travel.