This doesn’t answer your question totally, but maybe it will help…
For fun, sometimes I link up a Nintendo DS (with Korg DS10) to my DJ setup.
What I do is run Djay Pro on an iPad, then push that sound through a controller (Numark DJ2Go2 Touch), then a MakerHart JustMix 3 channel mixer. Djay Pro goes in ‘aux’, a microphone to ‘channel 1’.
I use a headphone splitter for the DS, with 1 cable to a mixer and 1 left open for headphones.
All beatmatching needs to be done by ear. Going DJ → DS is harder, you have to manually slow/speed up the BPM on Korg DS10 until it’s in sync. But you can only do that by like 1bpm/2bpm otherwise it gets hard to slow it down quickly enough when it’s in sync.
I try to be careful and only mix in to a longer track (or keep at the same BPM for several tracks) because it’s fiddly. Mixing out from DS to Djay is easier because you can nudge the record faster/slower so just manually beatmatch.