How can I trigger playback via MIDI

Afraid not natively, but you might try the following, if you don’t find it too limited or convoluted.

One limitation would be that if the PLE can’t find the name the of macro, such as if you rename or delete the arranger part, the macro will still play, since we don’t have if/then in macros or PLE.

Also you would need to test it to make sure it’s rock solid in performance. (obviously!)

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Set the parts to 1 Repeat, and “Pause after Repeats”

Create Project Logical Presets to search for each Arranger Part, select them, play them:

PLE:
Name | Equal |
Function: Select
Macro: Play Arranger Part

Create Macro called “Play Arranger Part”
Transport - Locate Selection
Transport - Start/Stop

The PLE preset will be available in the Generic Remote at Command>Process Project Logical Editor

This should play the section and then stop.