I understand what you are asking for however it isn't possible in the current product. There isn't an option that allows you to set the "end time" from last modified date to something else. Doing this sort of retro calculation can create issues for compliance calculations too so in general it isn't a good idea.
I tried the same using a service target for our dummy service. That' s also a possible option for our service desk.
I changed the service in status "Closed". The service targets of both services are in the same service target group.
The behaviour now is more like we expect, but obviously there's a bug with the SLM status.
The SLM status is calculated as without target. But in the SLM detaisl everything is fine. See screenshot