Another way of thinking of value-pricing is as "fixed price contracting, with the price based on benefit and ability to pay" rather than "fixed price contracting, with the price based on my input costs".
It's simply a switch from pricing based against your own costs, to pricing based on their resources and how valuable, i.e. how useful, your deliverables are to the client organisation.
A client's profits are an easy way to denote value to a client. But it's not the only way. What you need to be able to do is relate their revenue to their own deliverables. And then relate your deliverables to their ability to deliver.
Another key point to note: profits are leveraged from revenue - a small change in revenue can make a huge change in profits, if there is no change in the cost base.
There is no equivalent leveraging effect in play in an NGO. So you are probably going to have to look at the effect of your work on their cost-base. e.g. Can they double their work-output in a particular area, while only increasing their costs in that area by 5%?
Ideally, you are looking for ways that they can increase their productivity, their production efficiency, in a particular area, while lowering the costs in that area. Then you can attempt to model how much money they might save, and then put in for X% of that saving.