(Source: I'm the author of the ActiveInbox Gmail extension, and at various times have spoken to Gmail engineers directly).
I agree a service would be a useful thing. A killer bit of value would be if it could workaround Mozilla's addon rules. (We actually stopped publishing on Mozilla addons, because if Gmail changed, we couldn't wait 10 days to be "re-approved" to fix it, and as mentioned by gkoberger, Mozilla really clamps down on dynamic in-app updates).
Ymmv, but if it helps... From the POV of an extension developer, service reliability is critical, and I'm not sure if there's enough GMail extension developers to be customers and make it economically viable?
If there is, I think the ideal service would taint DOM elements with class names to make the important things selectable (rather than a Javascript API to retrieve elements). That way, we could build our own selectors with fail safes to fall back on (and we don't have the security headache of incorporating your dynamically-updated code within our own protected sandbox. We can just share the modified DOM instead).
Whatever you do with it, I'm really impressed with how cleanly you built this kartikt!
Also maybe it doesn't really have to be a service. It could just be a file on github, where anyone could issue a pull request if gets broken broken. That way way you would essentially crowd source it.
Also, I've personally been in contact with people on the Gmail team about this kind of stuff. They are, generally, supportive, but they're very clear that they'll make no guarantees about stability.
That being said, you should be able to use this to load new selector strings for the API:
https://addons.mozilla.org/en-US/developers/docs/sdk/latest/...
(For people who don't know, all GMail's classes and IDs are things like '.xb3', and they change often.)
Having worked on Mozilla Add-ons for a long time, one of the biggest problems was by the time any G-Mail add-on was approved, it was already out of date again. API calls, when done correctly, are allowed by both Chrome and Firefox -- this could be a good solution.
(You could easily charge a few bucks for this, and even contact Firefox + Chrome about making sure the reviewers allow it. Market it as "cutting down on their time" since there will be less to review.)