This may be an option I'm missing somewhere. I like the idea of having the donation widget, but the primary way people will be donating is by purchasing subscriptions or one-time items in the store.

Is there a way to flag a product/subscription as a donation item such that it automatically bumps the donation goal or would this need to be done via a service like Zapier once all of the commerce interactions are present?

There isnt a way in which to do this, unfortunately. You would need 3rd party development in order to achieve this.