@MWDelaney No guarantees, but this appears to work in my tests.
# run commands in local machine Bedrock `site` dir
composer remove johnpbloch/wordpress
composer require johnpbloch/wordpress:4.7.3
# git add..., git commit..., git push...
# run commands in local machine `trellis` dir
# edit `production` to be your <environment>
# edit `example.com` to be your site name
ansible "web:&production" -m command -a "composer clear-cache" -u web
ansible-playbook deploy.yml -e env=production -e site=example.com -e 'project_copy_folders='
If you have customized
project_copy_folders, just temporarily remove
vendor from your
project_copy_folders and run
deploy.yml (instead of using
-e project_copy_folders= in second command above).
Edit: Added quotes around