If you have cheap options you can try to exercise them early (before the delta is big) and/or in small chunks over time so you don’t get hit with the AMT.
This is one area where I think the company didn't make the consequences clear. But I also understand that they were trying very hard to not appear to be giving tax advice. Also, my company specifically asked us NOT to do small purchases. I guess there were people doing monthly exercises with each paycheck and the company didn't like that (it wasn't forbidden, just frowned upon).