Is there a way to import a PCB layout from one "sheet" into a multisheet in KiCad?
Kinda. File &gt; Append Board... to get something like this:-

and in 3D viewer you can clearly see 2 PCBs:-

The trick is that both the schematic editor and PCB editor have to be opened 'stand alone'. You can't use the top level command utility and work within a project. It all has to be stand alone. File &gt; Append Board... isn't on offer either if it's a project.
I didn't re-annotate the schematics (as that would mess up my stuff) but seems to work. You will see that components now have the same reference ID (C1 &amp; D1  for example). It's not ideal and you'll have address this manually. But there's the picture evidence above.
I guess that you then relocate existing laid out areas from PCB and scrap the other PCB.