Recurring Invoices - how not have tickets with recorded time @ $0 / hr ignored?

I need to keep track of ticket time, so I have a labor item @ $0 / hr price. How can I keep these from automatically being included on recurring invoices? I can just set the invoice to not automatically include - BUT I want tickets with billable time included and I don’t want a huge and growing list of “unbilled” tickets that show on invoice edit screen.

For us, our customers are AYCE, so we don’t charge the time log. This creates time on the ticket but doesn’t charge it so it won’t go to invoicing as a $0 item. You could also play with a status like “Resolved - Do not bill” for completely $0 tickets, but that won’t work well with a mixed ticket.

I guess the thing to do is click to un-charge time entries. What’s another couple clicks at this point?