In any plan, include some minor tasks that can be dropped if you get behind. You can always add more stories later and deliver more than you promised. It is important in an atmosphere of distrust and broken promises to meet your commitments. A few met commitments go a long way toward rebuilding relationships.
In Iceland, one of the winter sports is taking monstrous trucks bouncing around the backcountry. These trucks all have four-wheel-drive; but when they are out crashing around, they only use two-wheel-drive. If they get stuck in two-wheel-drive they have four-wheel-drive to get them out. If they get stuck in four-wheel-drive they're just stuck.
I remember two conversations: one with a middle manager who had one hundred people reporting to him and another with his executive manager who had three hundred people in his organization. I suggested to the middle manager that he encourage his teams to only sign up for what they were confident they could actually do. They had a long history of overcommitting and underdelivering. "Oh, I couldn't do that. If I don't agree to aggressive [i.e. unrealistic] schedules, I'll be fired." The next day, I talked to the executive. "Oh, they never come in on time. It's okay. They still deliver enough of what we need."
I had been watching first-hand the incredible waste generated by their habitual overcommitment: unmanageable defect loads, dismal morale, and antagonistic relationships. Meeting commitments, even modest ones, eliminates waste. Clear, honest communication relieves tension and improves credibility.
You can structure slack in many ways. One week in eight could be "Geek Week". Twenty percent of the weekly budget could go to programmer-chosen tasks. You may have to begin slack with yourself, telling yourself how long you actually think a task will take and giving yourself time to do it, even if the rest of the organization is not ready for honest and clear communication.