How much brighter is it at the end compared to the beginning? If it is more than, say, 4 stops, the beginning of the exposure might just be irrelevant, as the ambient light is usually ignored in exposure calculations with studio strobes, because the strobes are so much brighter unless a very long shutter speed is used.

Alternately, if the first part of the exposure is enough to bring the emulsion up to the threshold of exposure, then perhaps you might try to compute it like you would a pre-flashing exposure, except that the pre-flashing effect would only be relevant for the brighter parts of the image.