This tangential issue in StackOverflow shows actually how to define an own ONNX Session outside Piper TTS, and then pass it to the PiperVoice instance. This could solve the issue with multiprocessing (can't pickle the ONNX session)
Also, explains that ONNX already manages its own threads already. Maybe it's not worth to make it work in a separate Process.

Basically what I'm trying to do but full offline and already polished.
Only in English, they encourage tinkering

Voice, translation and conversational interfaces with a Python SDK that also offers ONNX models, and that looks promising

The example solution in this StackOverflow answer appears to me clear and easy to understand. For my Piper TTS case, try to initialise the worker and have the run loop accepting something to say. Do the same with the eInk and add them all into a Manager. Put in the queue text to say/display, but not a function to execute.

A fast and local neural text-to-speech engine that embeds espeak-ng for phonemization.
Development has moved here. Check if this is what I'm using.

Just in case of running into something like this while tinkering with TTS