Although Enterprise Architecture is key for many organizations, measuring success and seeking funding and acceptability across other functions is always a challenge. How have you navigated through this?

First, to be honest, I do not have a profound personal practical experience with this "issue".
Second, in an area like this I do not believe in easily computed KPIs based on easily gathered numbers.
So, I would mostly rely on "360 degree stakeholder satisfaction survey" - how different parties in the organization prize the contribution of EA to their and overall business.

A good EA should call out the business challenges in it's current state, giving business stakeholders an opportunity to participate and a voice in the exercise It should be a strategic discussion, customer/community focussed and information centric. This helps to get the business buy-in and funding as part of the budget process. As far as measuring success goes, as part of the EA exercise - it is critical to create an ICT roadmap that is aligned to the business objectives. This helps the EA to stay on track of issues, challenges and milestones and helps to measure goals, KPI's, etc.