One illustrative method disclosed herein involves, among other things, forming trenches to form an initial fin structure having an initial exposed height and sidewalls, forming a protection layer on at least the sidewalls of the initial fin structure, extending the depth of the trenches to thereby define an increased-height fin structure, with a layer of insulating material over-filling the final trenches and with the protection layer in position, performing a fin oxidation thermal anneal process to convert at least a portion of the increased-height fin structure into an isolation material, removing the protection layer, and performing an epitaxial deposition process to form a layer of semiconductor material on at least portions of the initial fin structure.