Google Analytics events to Marketo?

We see a value in getting Google Analytics events sent to Marketo, tied to the contact in Marketo.

What we have to play with is GTM and Big Query, and the munchkin script run on the site.

What would be your approach? I've seen ideas with pushing the lead id as a custom dimension to GA but how do you then get the data to Marketo?

List import isn't really an option unless it can leverage upon either GA CoreAPI or Big Query, since we cannot have a manual process in between.