Conjunction analysis: bootstrapped laterality?

Pretty old and frequently discussed topic aside:

I have 3 naming tasks presented in different sensory modalities (audio prompt, visual prompt, description). I am interested in what regions are most active across all three tasks. Further, for a given ROI, I would like to answer the question of which hemisphere shows more activity across all three tasks, a la laterality index (LI). All three tasks have been 3dDeconvolve'ed separately.

I was wondering if the following approach sounds sane:

I was thinking of following the old conjunction analysis approach, simply counting up all voxels that are active across all three tasks at a given threshold. To make it more robust, I could iterate across several thousand thresholds and take a trimmed average of voxel counts, a la bootstrapping. The final result would be a bootstrapped LI telling me which hemisphere was more active in a given task.

Does this sound like a reasonable approach to my research question? Would it be better, instead, to 3dDeconvolve all three tasks together and explicitly model a conjunction effect? If so, how could I calculate a robust laterality statistic for the conjunction effect?

Any expertise would be greatly appreciated!

The concept of a conjunction approach doesn't align with my preferences. It heavily relies on statistical thresholding and lacks the incorporation of valuable neurological insights. I prefer to concentrate directly on the magnitude of the BOLD response. Is it possible to anatomically define the region of interest in your context? If that's an option, how about comparing the response profiles between bilateral regions for each participant?