What to do with existing contacts in a flow when you need to retire the flow and enable a new one?

When you have an existing multi-email flow that’s been live for a while, but you now need to change it to a brand-new flow, what do you do with the existing contacts who are already in the (old) flow…

Is there a way to “block” all contacts from being triggered into a to-be-retired flow? In an ideal world, the existing contacts in a to-be-retired flow could still “finish out” from their current place within the flow, but yet the flow would not allow any new contacts to enter it (because I want all new contacts to get triggered into the new metric-triggered flow instead of the old segment-triggered flow).

It would be nice if there was an efficient way to “salvage” the contacts who are still in the old flow, so that we don’t just cut them off mid-flow.

Right now, I am changing all statuses of emails in the old segment-triggered flows to “Draft” because I don’t know how else to halt the flow from triggering more contacts into it.

Anyone have any tricks or advice to handle this?

MORE CONTEXT:
We found out (the hard way!) that segment-triggered flows can take 15 minutes or longer to trigger a contact and send the first email in the flow. (This delay is not ideal when the customer requested content from us and is expecting an immediate email response.) Long story short, we wired up some API that generates a custom metric on the customer’s contact record activity “timeline” from which we will now be triggering these flows (now metric-triggered vs. segment-triggered). We are working on rebuilding all of these multiple-email flows as metric-triggered flows, because, of course, we cannot clone a segment-triggered flow and magically change it to a metric-triggered flow. 

Because the segment-triggered flows have been live for some time now, we have existing contacts in waiting throughout these flows. As I rebuild and “enable” each of the new metric-triggered flows, I want to “disable” the corresponding segment-triggered flow so that no new contacts are triggered into the old flow from this point forward, but I’d still like the existing contacts in the old flow to complete the flow.

Thanks!