Having never developed for Android, I'm afraid I'd be of limited help, so take this with a grain of salt.
I see three options, the hard way writing from scratch (re-inventing the wheel)
A second option which combines existing tools with a minimal wrapper written by yourself, for which the basic components you would need are:
- A DOM Parser
- JavaScript engine (e.g. V8)
- wget
The last option would be to go the way of NVDA. And it might be worth working with them directly on something like this.
I'm not familiar enough with the inner-workings of NVDA to speak on their methods specifically, however it is a rather successful project and a working model of what your trying to do, albeit on a different platform.