Thank you, Gang. That helps immensely; I mainly needed help clarififying exactly which hypotheses I would be able to test with each approach.

I have also found that the statistics could have been inflated for the combined-test because I forgot the account for other stimuli that were present (stimuli in which we have no interest at the moment). I designed the matrix so those other stimuli would be dumped into the baseline, instead of accounted for with their own parameter, whereas in the individual-item case every stimulus was accounted for by a parameter. This could, I believe, have contributed 'noise' to the baseline parameter that could have affected the results of the test.