Is there a recorder that will do this?

[ajm]

FYI: This topic was originated in 2016.
The last post up until yesterday was almost a year ago in 2017.

For the record on Tascam: AFAIK Tascam no longer offers CD drives or MIDI on any of their self contained Portastudio recording systems.

Why not?
Beats me. If they did, I'd have bought a new DP24 or DP32 to replace my ancient 788 by now.
But that's another rant (which has been covered here before).