As in real life, you shouldn´t be able to carry fireplace in your backpack. You should but rags+sticks ot of backpack and craft it there, which would place fireplace on the ground. It would be fixed on that place since then, and couldn´t be possible to put into inventory.

You would have to eiher: - Create new fireplace everytime you move

• Stay at one location where you know fireplace is

That would be best with fireplace as persistent object (Already mentioned by Rocket i think), which would be some icon of survivors around in location.

At the end, I love fireplaces, you did excelent jobs!