How does ICA handle inevitable delays in signals?
One of the most successful uses of ICA has been in the study of electrophysiology (i.e. brain activity), principally EEG (Electroencephalography) and MEG (Magnetoencephalography). They are used to remove artefacts (such as electrical impulses caused by muscle movements (eye blinks etc)) without the need for reference channels. In this application the spatial separations between sensors is minute compared with the propagation speed of the waves, and as such the assumptions of ICA effectively hold. 

For fMRI, which relies on blood flow in the brain, the temporal delay issue is more significant. One approach, taken in the paper Latency (in)sensitive ICA. Group independent component analysis of fMRI data in the temporal frequency domain by Calhoun et al (2003) attempted to solve this problem by making estimates of the time delay in each voxel, and then using this as prior information in a modified ICA. Maybe something like this could be applied in your domain?