Thermal desorption spectroscopy is employed to examine transport mechanisms in structured, nanoscale films consisting of labeled amorphous solid water (ASW, (H2O)-O-18, (H2O)-O-16) and organic spacer layers (CCl4, CHCl3) prior to ASW crystallization (T approximate to 150-160 K). Self-transport is studied as a function of both the ASW layer and the organic spacer layer film thickness, and the effectiveness of these spacer layers as a bulk diffusion "barrier" is also investigated. Isothermal desorption measurements of structured films are combined with gas uptake measurements (CClF2H) to investigate water self-transport and changes in ASW film morphology during crystallization and annealing. CCl4 desorption is employed as a means to investigate the effects of ASW film thickness and heating schedule on vapor-phase transport. Combined, these results demonstrate that the interlayer mixing observed near T approximate to 150-160 K is inconsistent with a mechanism involving diffusion through a dense phase; rather, we propose that intermixing occurs via vapor-phase transport through an interconnected network of cracks/fractures created within the ASW film during crystallization. Consequently, the self-diffusivity of ASW prior to crystallization (T approximate to 150-160 K) is significantly smaller than that expected for a "fragile" liquid, indicating that water undergoes either a glass transition or a fragile-to-strong transition at a temperature above 160 K.