The properties of two-dimensional (2D) transition metal dichalcogenide (TMD) monolayers can be dynamically controlled via strain-induced displacive structural transformations between semiconducting (H) and metallic or semimetallic (${\mathrm{T}}^{\ensuremath{'}}$) crystal structures. The shapes, symmetries, and kinetics of crystalline domains generated during these transformations and the mechanical response of transforming monolayers are of fundamental and applied interest in, e.g., phase change memory devices and the study of topologically protected edge states in quantum spin Hall insulating ${\mathrm{T}}^{\ensuremath{'}}$ crystals. We quantitatively characterize ${\mathrm{T}}^{\ensuremath{'}}$ domain morphologies during $\text{H}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}{\mathrm{T}}^{\ensuremath{'}}$ transformations in both flat and bendable TMD monolayers using a combination of first principles and continuum calculations. Wulff constructions for ${\mathrm{MoTe}}_{2}$ and ${\mathrm{MoS}}_{2}$ show that ${\mathrm{T}}^{\ensuremath{'}}$ domains within much larger ${\mathrm{T}}^{\ensuremath{'}}$ domains are either rhombi of fixed proportions (if nonmisfitting) or rectangles whose aspect ratio ${A}_{R}$ increases with domain size ${L}_{0}$ (if misfitting). Isolated ${\mathrm{T}}^{\ensuremath{'}}$ domains within much larger H domains undergo a morphological crossover from compact to elongated shapes at ${L}_{0}\ensuremath{\approx}100\text{--}200$ nm if the sheet is constrained to be flat or ${L}_{0}\ensuremath{\gtrsim}2\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$ if the sheet is free to bend. This crossover is driven by a competition between anisotropic interfacial energy and elastic misfit energy, and its position can be tuned via the monolayer-substrate interaction strength. It is shown that the aspect ratio ${A}_{R}$ obeys a scaling law ${A}_{R}\ensuremath{\sim}{L}_{0}^{2/3}$. Stress-strain response characterized as a function of strain orientation reveals extreme anisotropy in the effective elastic modulus through $\mathrm{H}/{\mathrm{T}}^{\ensuremath{'}}$ coexistence. Ferroelastic multidomain ${\mathrm{T}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{WTe}}_{2}$ monolayers are found to exhibit two to three regimes of reversible mechanical response, and localized buckling in freely suspended ${\mathrm{T}}^{\ensuremath{'}}$ monolayers is shown to qualitatively alter ${\mathrm{T}}^{\ensuremath{'}}$ domain symmetries.