Welcome to the Meteor Forum! 
You can easily integrate the bpmn.io modeler into your applications.
Regarding an engine I can suggest you to use https://github.com/paed01/bpmn-engine
Which is working great and has 100% coverage for the current set of features.
I also created already an organization on GitHub cquencial which aims to integrate this engine with Meteor on a modular basis but got stuck lately due to other projects. Would appreciate any of your feedback there with an issue or even a PR 
Edit:
I also created an AutoForm extension to integrate the modeler with a properties panel: https://github.com/jankapunkt/meteor-autoform-bpmn
But it uses an older version and I also had no chance to update it recently.