I did some research and you are indeed correct about the Zapier connection. Unfortunately that is an outdated plugin, therefore bugs might occur. If I understood correctly you would like that the two platforms (Wordpress and Contentful) could exchange data and then you will be able to migrate your blog gradually, however that might be too complicated for your goal.
Our suggestion would be to either connect you wordpress with Contentful using our official PHP SDK:
But I imagine you will need to build your own plugin and/or controller to manage the Contentful entries in Wordpress.
The other solution would be to migrate completely to Contentful, it would require a little more work, but it’s probably worth to maintain only one platform. We have few articles about: