The current implementation of this is cumbersome and convoluted:
This, in my oppinion should be “baked” into the helpdesk.
This new workflow will cause more harm the solve issue in the long-term.
Creating re: tickets, or follow-ups should be straight forward, and somehow “baked” into the product itself.
Any customer reply that comes on a CLOSED ticket, should create a re:/follow-up/split ticket(whatever you want to call it), copying pretty much all the details from the original ticket, into the new one, and just giving it a new ticket id/reference.
Zendesk does this quite well.