Design space exploration (DSE) for Text-to-Image (TTI) models entails navigating a vast, opaque space of possible image outputs, through a commensurately vast input space of hyperparameters and prompt text. Perceptually small movements in prompt-space can surface unexpectedly disparate images. How can interfaces support end-users in reliably steering prompt-space explorations towards interesting results? Our design probe, DreamSheets, supports user-composed exploration strategies with LLM-assisted prompt construction and large-scale simultaneous display of generated results, hosted in a spreadsheet interface. Two studies, a preliminary lab study and an extended two-week study where five expert artists developed custom TTI sheet-systems, reveal various strategies for targeted TTI design space exploration—such as using templated text generation to define and layer semantic “axes” for exploration. We identified patterns in exploratory structures across our participants’ sheet-systems: configurable exploration “units” that we distill into a UI mockup, and generalizable UI components to guide future interfaces.