hmm, saying it aloud to myself, it seems that the zz does indeed become more of a [ts] affricate, as in [pitsa] for pizza. It has also stimulated my appetite
however, the ッシ is just an elongated fricative [ːɕi], without the "stop" present in an affricate; as far as I can see, the closest affricate approximation of the double z would be ッヂ/ッジ, [ʥi], which is almost identical except for being voiced and its placement. I'm not saying that's how it is in common usage, but I'm just interested in the way foreign sounds are adopted and transliterated into Japanese. It seems that certain aspects of a sound take precedence over others when choosing how it should be reproduced with Japanese sounds.
Maybe it's time to send an email to my old phonology professor...