It would really be nice to have this work, and maybe sometimes it will work by having a discreet conversation with a trusted manager. But that's not a sure-fire thing. For all you know they're done having layoffs.

Another idea, you could see if the company might be open to an unpaid sabbatical.

The only sure-fire solution in my mind is to get another job, and the way to make that into a break is to set your start date later. Most employers don't even mind a start date that's around a month into the future.