Hi @Matt Tebbs,
Reading your business requirements, I think it could be quite tricky to archive in Genesys Cloud. I do not said it is not possible, if it doable could be quite resourceful.
Maybe the community could share more insight about digital interactions works in Genesys Cloud, so far, to my understanding with digital interactions are already assign to an agent as long the thread timeline is active, any new reply from customer will not enter to the queue, it will directed to the assigned agent, only new interactions will go to the queue or through a email flow. So, if in the middle of a conversation the email context change to be considered to "level up the priority", I think it will not be a way to do something about it, at least with architect. Maybe a way, using real-time transcription? An external process receive the transcription of the last reply, and after analysis send a notification to the agent to go to the interaction.
If the interaction is considered by the engine routing a new reply (outside the thread timeline), the interaction should go to an email-queue, so you can use an email in-queue flow to check the last content and look if it need to "adjust" the priority, try to be assign to the same agent or another and send some notification.
On the other hand, with trigger you have some options:

Where you could use topics to findout when a email could be considered to change priority and take some actions.
Hope this give you some ideas.
Regards,
SG
------------------------------
Saugort Dario Garcia
Arquitecto de soluciones
e-Contact
https://www.e-contact.cl/------------------------------