Route A: Easiest route would be to combine all of your Songs in a single desktop iTunes library, perhaps in a Music account. From here make use of a single Apple Id for library and iphones - this will work, the question is does it meet your need?
Current Situ: The issue your current pattern of use hits, as Michael has shown, is that you are in danger of needing to support more than 1 Apple Id per device - this is simply not possible with the current Apple Service.
Route B: To create separate libraries would suggest that you use a further computer - you can than run 1 set of computer, iphone and iTunes Match subscription discrete from the other - this will also work - transfer of Songs between the libraries will work well via audio CD export / import at 256 kbit AAC.
Summary: In summary move from Current Situ to either Route A or B, pending your need.