One thing I notice people getting overthinking in the compos is figuring out the keys of the tracks they have to arrange together. In my opinion (as the guy that conceived the source-versus-source style compo), figuring out the actual key is far less important than figuring out the mode, regardless of what the tonic is. It doesn't matter if one of the sources is in Bb Minor and the other is in F Minor. The Bb and the F don't matter. What matters is that the two tracks are in the Aeolian mode (aka natural minor). When the mode is common, it's incredibly easy to make the sources work together with each other, you just transpose the material from the sources (melody, chord progression, etc.) into a common key, like C minor or something.
It gets tougher when you have something like Ionian (aka major scale, e.g. C major) and Aeolian (e.g. D minor) sources being combined. Now you have to think about how you want to push them together. Do you flat the third, sixth, and sevenths of the Ionian source's melody so that it's Aeolian now (i.e. play a C major song in C minor) and then transpose to a common key? Do you keep the Ionian source Ionian (e.g. C major) and shift the tonic of the Aeolian source down to the relative minor (i.e. A minor)? These are options and techniques you can use to push two different sources together and keep them from clashing.
Remember, you can write an arrangement in any key you want. A song can be played with any note as the tonic. Think about the classic Star Wars melody:
G, D, C B A G, D
Except you shouldn't think of it that way. You should think of it as:
1, 5, 4 3 2 8, 5
Where 1 is any of the twelve notes.
C, G, F E D C, G
Bb, F, Eb D C, Bb, F
You see what I'm getting at? Worry less about the tonic and more about the intervals and relationships between the notes and where they fall in the scale. When you start thinking about melodies and chords that way, one of the barriers to doing multi-source arrangements disappears.