Thanks Matt, a good suggested line of action. You have helped me confirm what I suspected. We can create an an [external_tool] assignment, but realistically we would then have to manually select and save the specific Turnitin LTI tool configuration we want to use for the assignment (we have more than one). This isn't so bad because as you have pointed out Turnitin's long list of 'optional settings' can be saved as the default in your Turnitin profile.
These are the results from an existing LTI assignment - the 'external_tool_tag_attributes' are evident, but only the 'new_tab' might be changed generally:

And these are the current settings that Turnitin will pull in from Canvas:
custom_duedate=$Canvas.assignment.dueAt.iso8601
custom_startdate=$Canvas.assignment.unlockAt.iso8601
assignmentid=$Canvas.assignment.id
custom_submission_title=$Canvas.assignment.title
custom_maxpoints=$Canvas.assignment.pointsPossible
are synced with Canvas equivalents initially we will have
Kind regards
Jago