Vic,
That is an interesting question. The answer is that you really are ahead of me in this.
But what it seems is going on is that when you turn on the effects, you are sending part of the "arranger" signal and part of the "vocal" signal to the DSP chip which returns the stereo signal to both outputs.
Therefore, when you turn off the DSP from the vocals, you shut down the mix return from the DSP.
Here are two suggestions:
1) It may not work but it is a worth try. You know there are two Independent DSPs. So if you can select one of them ONLY for arranger and the other ONLY for vocals, this might solve the problem.
2) Do not record at the same time but record instead in tracks! First record the arranger stuff and then record the vocal stuff (not at the same time). I know this is not what you are looking for but consider the following, I usually work with 16 tracks from the keyboard, and I download one track at time to my Studio!!! It takes forever... I know