Applying elastic deformation can tune a material's physical properties locally and reversibly. Spatially modulated lattice deformation can create a bandgap gradient, favoring photogenerated charge separation and collection in optoelectronic devices. These advantages are hindered by the maximum elastic strain that a material can withstand before breaking. Nanomaterials derived by exfoliating transition metal dichalcogenides (TMDs) are an ideal playground for elastic deformation, as they can sustain large elastic strains, up to a few percent. However, exfoliable TMDs with highly strain-tunable properties have proven challenging for researchers to identify. We investigated 1T-ZrS2 and 1T-ZrSe2, exfoliable semiconductors with large bandgaps. Under compressive deformation, both TMDs dramatically change their physical properties. 1T-ZrSe2 undergoes a reversible transformation into an exotic three-dimensional lattice, with a semiconductor-to-metal transition. In ZrS2, the irreversible transformation between two different layered structures is accompanied by a sudden 14% bandgap reduction. These results establish that Zr-based TMDs are an optimal strain-tunable platform for spatially textured bandgaps, with a strong potential for novel optoelectronic devices and light harvesting.