Ok I figured this out, and maybe it should have been a bit more obvious. The Tempest is not just only 6 Voices, it only has 6 notes of total polyphony for sequencing. When you assign your Sounds to specific Voices, and use the individual outs, each channel "owns" one of those notes of total polyphony and you effectively have 6 monophonic sequencers, one per voice out. In my case today, I was using all 6 channels in the Beat already. 1, 2, 3, 4 are kicks, snare, hats, percussion, some atmospheres on 5, and basses on 6. Because all 6 voices were actively being used in the Beat, there was no polyphony left to assign another sequence to without stealing notes.
The work around is to share the external sequencer pad's voice channel with Sounds that you won't use at the same time. In my case I could have assigned it to channel 5, muted my atmospheric patches, and have the pad sequence going after that.
Still a bit of a letdown, but now I understand why it's happening. Mysteries are more frustrating than things I can explain, so I'll live with it, and carry on. And look for a cheap Digitakt for external sequencing.