I decided to limit the scope of the adventure in terms of both location and time. The adventure plays out over the course of one month, with each round (upkeep-move-encounter-Mythos) representing the passage of one week. I decided to use a list of Mythos cards I'd already drawn (from a different writing project) because I didn't have any Mythos cards on hand when I began this experiment.
Based on the Mythos cards I drew (namely, Fourth of July Parade!), the Unnameable and the River Docks (and thus, Pete) will be completely inaccessible for the first "week" of the adventure. This is cool with me, as the player character(s) will still have three great locations to examine: the Witch House, where there's an open gate, or either the Woods or the Black Cave, where there are two clues each.