Follow-up: In case others need the information, a helpful redditor found a workaround. It turns out you can still multitask in Game Mode (as opposed to Desktop Mode). Press the Steam button, select Library, and start a different game, preferably something lightweight in memory. Once it's started fully and music/controls are functional, press the Steam button again, navigate to the new game, and select 'exit game'. Focus will switch to Fallen Enchantress and just like the old alt-tab method, the game will now be properly focused and the main menu will highlight and be usable as normal.