Lateral move after 3-4 years in strategy consulting?

Hello,

Looking for advice, anecdotes or words of caution regarding moving firms after 3-4 years, whether it be before or during business school. And if you don't think it's possible, I'd be interested to hear why.

I'm currently at a strategy firm (think Vault Top 10 but not MBB or Big 4) and have had a great run, but am fed up with my firm's culture. It's very homogenous and a bit toxic if you aren't a white guy who went to Dartmouth, though the real issue is that HR responds poorly and vindictively to any issues that people encounter, whether it be normal things like burnout or really serious stuff like harassment. In general, HR/Talent and Partners are just in "cover our a**es" mode, and now feel like adversaries to most Associates/Consultants/Analysts/etc.

I'm currently planning on leaving for school in fall 2018 (on sponsorship; I'm already at post-MBA title and salary which I imagine could make this harder or easier), so I'm wondering whether it's best to stick it out and recruit at other firms whilst at bschool or if it's possible to transition before that. I'd be open to delaying bschool for a year if necessary.

Any advice or anecdotes would be very appreciated.