One very effective approach is to grow the tree more slowly. That is, instead of expanding the tree every time you reach a leaf node, you expand it once it has at least k visits. This will significantly slow the growth of the tree, and often does not reduce performance. I was told by one of the authors of the Fuego Go program that he tried the approach, and it worked well in practice.
This idea was originally described in this paper:
Remi Coulom. Efficient selectivity and backup operators in monte-carlo tree search. In Computers and games, pages 72–83. Springer, 2007.
It was also used in:
Max Roschke and Nathan Sturtevant. UCT Enhancements in Chinese Checkers Using an Endgame Database, IJCAI Workshop on Computer Games, 2013.