The main problem is that depending upon which definition is being followed Irreducible complexity itself can either allow or disallow normal evolutionary pathways.
The initial definition by Michael Behe, 'By irreducibly complex I mean a single system which is composed of several well-matched, interacting parts that contribute to the basic function, and where the removal of any one of the parts causes the system to effectively cease functioning.', is a perfectly usable definition and while it has a degree of subjectivity is probably quite sufficient for most people to agree on a number of things as being IC. The problem for the ID camp is that Behe's original definition has nothing to say about the evolvability of such systems. Behe uses their existence as an argument for another mechanism to be involved, but gives no compelling reason why already understood evolutionary mechanisms are not perfectly sufficient.
William Dembski then redefined IC in terms of his own concept of Specified Complexity and redefines it in such a way as to rule out plausible evolutionary pathways.
So we have two different froms, one which can be used but is useless and one which is not useless but is completely unusable relying as it does on numbers Dembski seems to have effectively made up off the top of his head and the ability to eliminate all natural evolutionary mechanisms as the source of the complexity, which seems rather redundant since if he could do that he wouldn't need to make an argument from SC/IC.
I don't think your system would produce a way of studying IC by either of these definitions. Your eventual minimal cell might be IC as Behe defines it but it doesn't preclude prior simpler forms the vital components of which have since disappeared from the genome.
TTFN,
WK