In turn-based multi-action adversarial games each player turn consists of several atomic actions, resulting in an extremely high branching factor. Many strategy board, card, and video games fall into this category, which is currently best played by Evolutionary MCTS (EMCTS) -- searching a tree with nodes representing action sequences as genomes, and edges representing mutations of those genomes. However, regular EMCTS is unable to search beyond the current player's turn, leading to strategic short-sightedness. In this paper, we extend EMCTS to search to any given search depth beyond the current turn, using simple models of its own and the opponent's behavior. Experiments on the game Hero Academy show that this Flexible-Horizon EMCTS (FH-EMCTS) convincingly outperforms several baselines including regular EMCTS, Online Evolutionary Planning (OEP), and vanilla MCTS, at all tested numbers of atomic actions per turn. Additionally, the separate contributions of the behavior models and the flexible search horizon are analyzed.