Am I missing something or is this the intended workflow? So many clicks.
Yeah, it's not ideal.
You can select any of the overlapping objects under the mouse cursor by holding the Tab key. Once you select the correct tilemap, you can start editing tiles - it will remain selected, so you don't need to lock the layer.
When I drag a tilemap from the Project bar into the layout, it copies the tiles I’ve drawn from another instance of that tilemap,
That's how objects in Construct work - new instances inherit properties from the first "default" instance. This also applies to instances created at runtime.
A common practice is to use a separate "Repository" layout for default instances, where you can configure them properly and not worry about changing them by accident.
Can I lock a tilemap’s position ONLY
I'm not sure this is possible.