You can call/render a Blaze template using a custom React component - see this example component from the meteor-webpack-react project. Just copy the component to your project, but delete the first import line and replace export default with BlazeTemplate = to export it as a global (I assume you’re not using webpack and/or ES6 modules). Then you can simply render any Blaze template you need anywhere from React with: -
JFYI the file seems to have changed since you linked to it, so here is a permalink to the version you referenced, and here is a gist with the s/export default/BlazeTemplate =/ change you suggested, that should be able to be dropped in to any Meteor project.