Not a fully-worked-out model, but here are some thoughts.

On methods:

• Progress studies is an integration of history, philosophy, and economics (and maybe other fields, but those are the big ones).
• I think history is the empirical foundation—where we get the case studies and the data from. That's why, when I wanted to understand progress, I started by studying how it has actually happened, and indeed before I even asked “how” I just tried to figure out what happened.
• Quantifying is good if/when you can do it appropriately. But make sure the thing you are measuring can actually reasonably represent the concept you are trying to study.
• In general, go deep on whatever you're studying and really get into the details. Your ratio of case studies to grand theories should be like 3–5 to 1.

On understanding vs. rhetoric:

• There are both factual questions and ideological ones (or perhaps a spectrum). The factual questions include: how does progress happen, what are the mechanisms and causes, how can we measure it? The ideological questions include: is progress actually good, and can humanity have any agency over progress in the future?
• Both are necessary and important, and I think the answers reinforce each other. The motivation for studying the factual questions is the conviction that progress is good and we can make more of it if we try. Conversely, when you honestly study the history of progress I think you can't help but conclude that it has been very good for humanity and that its legacy is worth defending.
• However, there is a trap here: promoting any ideology can put you in “soldier mindset.” Rather than honestly consider counterarguments, you can start to shut your ears, dig in your heels, and fight.
• So, I think we should hold ourselves to the highest epistemic standards. Keep an open mind, listen to criticism, steelman your opponents. Don't let progress studies turn into a dogma.

I suppose I would start with philosophy, with questions like....

Progress towards what?

Consider the Amish.    Generally speaking, the Amish have to one degree or another opted out of technological progress.   And so..

They don't have nuclear weapons.  They aren't contributing to climate change.  They don't experience all the negative aspects of modern society that we calmly accept as being completely normal.  

I'm sure this is an overly simplified view of the Amish, but I think you get the point.  The experience of the Amish demonstrates that technological advances, and progress, are not automatically the same thing.   In spite of their technological backwardness, the Amish have achieved a form a progress that in some respects is quite superior to our own.

Philosophy is, in part, a study of the assumptions underlying our behavior.  If some core assumption is unexamined, and to some degree false, then whatever we build on top of that assumption is likely to be in some way problematic.   The most efficient method of proceeding may be to examine our fundamental assumptions very carefully first, before investing vast resources in to some unexamined definition of progress.

Here's an example.   One of our most fundamental assumptions is that life is better than death.  Pretty much everyone takes this to be an obvious given.   And yet, there is no proof at all that this assumption is true.   And so, when we spend trillions on our medical system with the goal of saving lives, we actually don't have the slightest clue whether we're doing the patients a favor or not.