Trying to make a fair game out of this would be more of a challenge than the actual invasion itself I suspect.
The only thing I can think of is change history and actually have some Russians help the Tibetans. Younghusband invaded because he suspected Russian agents were at work, so he wouldn't be surprised to find them there. Alternatively they could rely more on their Kham cavalry. The Kham were wild Steppe Cavalry and less pacifist than the rest of Tibet. They still only had swords and old muskets though.
The 1950 Chinese invasion though could just about be made into a game. The Tibetan army had by then been remade into a nineteenth century one by then, so they were only 50 years behind the opposition rather than 300.