FutureCFO, I'm just a college student so I don't have any actual experience being recruited/leaving the Big 4. I imagine that you fill out the online applications and contact them for these positions yourself. I suppose you can hire a headhunter and they will find companies that would be interested in you.
Opportunities available for those with Big 4 experience including moving into internal audit for Fortune 500 companies or become a financial controller. A quick job search displanys many openings that require/strongly prefer those with Big 4 experience: Financial Controller - Big 4 Experience jobs in New York, NY - washingtonpost.com
It seems like a lot of those jobs are paying in the 80-110K range. Some of them even advertise leaving the stress/hours of the Big 4 behind explicitly.
I don't know how many accountants in this situation pursue an MBA but I've been told by family members who work in business that accountant/auditing --> financial controller experience + MBA degree is a pretty decent route to become a CFO if that is your ultimate goal.
Also becoming an accountant is not a typical route to get into IBanking, it would be difficult to break into. Also, I've read that Big 4 experience is often times not the type of work experience that the most elite MBA programs are looking for... idk if that's true or not but that's what I've heard. Basically, accounting is not the career path for you if you want to be an IBanker at a bulge bracket bank...