If I may make a suggestion though? You mentioned going book by book, most likely starting with the CRB and then going in order of release.
You have quite a few years of catching up to do however, so it will be a long time till you'll reach the recent books, and by then new stuff will have been released.
The bigger the windmill, the easier it is to tilt at....
The plan at this point, yes, is to hit Core and
Run Faster at the same time, since those are the two biggies for character generation. Then, yes, hit the splats in order of release, and then move on to other stuff.
No plan survives contact with the enemy, however, and I'm already seeing that we're probably going to be doing a lot of parallel processing. One of our guides is going to be the Missions FAQ, and it's got a lot of stuff in it. As we address it, there's going to be overlap with other books, so even at the outset things are going to be scattered about a bit.
We're not really going to be able to get started until after GenCon anyway, and that's in a couple weeks, so it'll probably be the middle of August before we really get going. And by then, the plan might change yet again.
I'm not quite sure how BattleTech does it, but I guess they don't start 3 or 4 years after the initial book release 
Pretty sure you're right, but I'm not sure how their current system actually got started. It could have been as a result of similar circumstances. I didn't ask; didn't seem pertinent why it got started the way it is, as long as it's a process that works and can be easily emulated.
Basically, they take rules questions from the forums. In their own little Fortress of Solitude, they have a team of knowledgeable guys look over the rules question, and figure out how to fix it. They talk to the guy who wrote it, when possible, to determine intent. Then they fix it. Then they publish the fix. Then they move on to the next one.
Emulating that, what I've outlined (and what may, like the order of things addressed, change drastically once we get into a groove with this) is this:
1. Identify problem.
2. Argue about problem.
3. Fix problem.
4. Publish fix for field testing.
5. Fix the fix later if necessary.
6. Repeat for next problem in the book.
Once a book is finished, it goes:
1. Gather all the field-tested fixes and put them into an errata document.
2. Get errata document laid out and looking pretty, since that's a big deal these days.
3. Post errata document.
4. Provide errata document and layout notes to Jason and Matt (the layout guy) to correct the PDF.
5. Post/update the PDF once corrections are made.
6. Breathe a sigh of relief when it's time for a reprint and corrections are already made.
All of this is, of course, subject to tweaking. As I said before, no plan survives contact with the enemy.
I hope that addressed some of your concerns.
