How offset are your columns? You'll likely find that the overwhelming majority of the information out there is predicated upon the kind of regular column layout that only seems to exist below grade these days. You might find something by googling Dr. Bijan Aalami. He founded the company that offers AdaPT, a popular PT design software package. I think that I've seen some design guides by him that deal with irregular layouts. The information should be similarly applicable to mildly reinforced slabs.
In my opinion, given the present state of computational power, FEM is the rational way to go for highly irregular column layouts. The middle strip / column strip rules become sketchy for irregular layouts. I also think that codes should relax some of the the moment distribution rules when FEM is used as the whole point of FEM is to determine realistic moment distributions. For better or worse, I'm already doing this in my work. I imagine the codes will catch up in time.
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I suggest that you become familiar with the Hillerborg Strip Method and the Yield Line Method. You can find lots of references for either method on the Internet. To start out with a yield line analysis, recognizing it is an upper bound solution, you should check it by Hillerborg's method before finalizing your design.
