I solved this issue in the end without using any plugin. The solution works because this is a multi-site install. The procedure is quite simple and painless.
- I created a ‘contact’ subsite on the subdomain ‘http://contact.example.com’
- I moved the contact ‘page’ from the main site to the sub site.
- I enabled comments on this new page, both in wordpress admin, and in the theme.
- I made the contact page the default home page for the contact site.
- I changed all links on the main site to the ‘contact’ form to this new page.
- I deleted the old page.
I receive email notifications for the ‘contact’ but not the main site.