Short-term, you could likely just use the scheduling capabilities in IronWorker and have the worker hit an endpoint in your application. The endpoint will then trigger the operations to run within your app environment.
Longer-term, we do suggest you look at more of a service-oriented approach whereby you break your application up to be more loose-coupled and distributed. Here's a post on the subject. The advantages are many especially around scalability and development agility.
https://blog.heroku.com/archives/2013/12/3/end_monolithic_app
You can also take a look at this YII addition.
http://www.yiiframework.com/extension/yiiron/
Certainly don't want you rewrite your app unnecessarily but there are likely areas where you can look to decouple. Suggest creating a worker directory and making efforts to write the workers to be self-contained. In that way, you could run them in a different environment and just pass payloads to the worker. (Push queues can also be used to push to these workers.) Once you get used to distributed async processing, it's a pretty easy process to manage.
(Note: I work at Iron.io)