> would it be incorrect to use glt with 3 factors?
No, there is nothing wrong with your specification because it's indeed a t-test. For example,
-glfLabel 4 3way_inter -glfCode 4 'group : 1*ctrl -1*temp & 1*ctrl -1*front phase : 1*acq -1*rev reinf : 1*corr -1*incor' \
would test the same hypothesis as the three-way interaction F=test that 3dMVM automatically provides except that the F-stat is the corresponding t-stat squared.
Gang