Criteria for a fiberwise Fujiki/K\"ahler family to be locally Moishezon/projective

Inspired by certain topics in local deformation theory, we primarily utilize F. Campana's methods to investigate how far a fiberwise Fujiki family is from being locally Moishezon and how far a fiberwise K"ahler family is from being locally projective. We investigate these questions from two main perspectives: cohomological data and global semi-positivity data on the total space.