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Not an exact answer to your question, but we have encountered similar difficulty.
Based on subject lines and From email addresses, we have been able to do some routing using Action Rules and Processes, but not actual data manipulation.
Conceptually, you could use the API to read in the details of new tickets and re-push the content of the custom fields. You would need to write the logic processor in the language of your choice, but that might be the most viable option.
Logic/Workflow (Timer Based)
Incoming Emails: Set to status of X
API GET: Pull All Tickets with status of X
for each ticket
API GET: pull detail
Parse Data into variables
API PUSH: Update ticket custom fields
API PUSH: Set ticket status to Y
That's my .02 anyway.