Hi Mike,
Welcome to the forum and thanks for posting about such an interesting topic!
One of the aims of Speckle, and particularly the new version we’re currently pushing out, is exactly to facilitate workflows like the one you describe. Since Speckle already does the hard job of extracting data from Revit, pushing it to a web app, displaying a 3D model in a viewer, etc, you just need to write a small web app that calls the Speckle API and computes the carbon cost.
The previous iteration of Speckle was actually used to demo an embedded carbon estimator, you can see a glimpse of it here (Arup might open source it at some point).
Anyways, building such a tool as mentioned already is a relatively simple task, @dimitrie who developed the app above can elaborate more!
P.S.
If you’d like, we have a section where you can Introduce yourself 🙆