Waterfalls Don’t Iterate
You cannot slave for two masters, you will love one and despise the other. Using a hybrid project management methodology (PMM) is like trying to slave for two masters. Attempting to cherry pick the “best” methods and practices from each to come up with the uber methodology seems like a good idea but often just leads to frustration.
Choose the tool that is best suited for the job. Personally I do not want a hybrid hammer-screwdriver. When I need a hammer give me a dedicated hammer. When I need a screwdriver give me a dedicated screwdriver. Stop the cross bleeding of Waterfall and Agile. Let your Waterfall processes and procedures stay there. For Agile, create processes and procedures that perhaps will generate the same artifact but are developed around a truly Agile process. (Yes, yes I know what the manifesto says)
Organizations should not feel that they need to settle on a single PMM. In fact I see more value in allowing your PMs to choose whichever PMM they feel is appropriate for the project. If the PM is accountable then let them decide which methodology is best for the project. If you are in a document rich organization that requires numerous artifacts then just mandate that regardless of the PMM that all project artifacts must be provided and the timeframe in which they should be provided.
Forego the hybrid mashup methodologies and instead embrace a culture of exploration. Be willing to let your PMs decide the best approach and support them in that decision.