One Master Page deployed across all Site Collections SP2016

My client has ~180 site collections in their SP2010 farm and are upgrading to SharePoint 2016. They want a solution where they build a single Master Page (based on Seattle) and then deploy it (and select it) for every site collection. This is doable (one option is creating each site collection using a site definition), but then they want to have some mechanism where each time the Master Page is updated, they want the changes to apply to every site collection.

I am thinking a code-based solution, but is there a simpler way? Can you have a web-application based Master Page that a Site Collection refers to, or must the Master Page reside in the Master Page Gallery? Earlier questions in this forum refer to earlier versions of SharePoint.