Is there a method to change the document being edited by Letters without destroying the editor and constructing it again?
It is not possible in the current version of Letters.
You need to ensure that you will not overwrite the document for other users when you collaborate with them. It means that you need to disconnect from the current document and connect to the new document. In the current version of the CKEditor 5 collaboration plugin (and in Letters) the editor connects to the document during initialization. This is why you need to destroy and create the editor to connect to the new document.