I've not gotten to do much programming. But when I have, I've liked to have a way to feed what I learn week-by-week back into the process as things go on, and to adjust things to keep the effect of misjudgements or the zillion little things that sneak in under the radar from piling up into the part of the project. As you work a project you usually develop a much better understanding about which features of a project are really important to the end user, which are costly to develop and to use, etc. This, coupled with progress information, could be adjust priorities, assignments, and estimates, if anybody had the time to think about it. It seems to me that schedule feedback when there is time and opportunity to do something with the information could be greatly appreciated, especially if it helps avoid the death march. "Padding" at the beginning (meaning trying to allow for details that are not explicitly in the plan) is helpful, but I suspect that continuous feedback and adjustment to the plan gets people to think a lot harder about what they are doing and how they are doing it.
As for charts with red on them... A lot would just depend on the tone of an organization. I've been very surprised at the degree to which "non-management" reaction to change is "this too shall pass". (I shouldn't be, since, all too often, it is true.) You might want to consider whether your gut reading of the environment is "we are all trying to learn to do this better", or "what we had was just fine, let's not rock the boat". Almost anybody is going to first turn red when they see red on their task. So what matters is whether people get stuck there, or get past the pain and on to how to solve the problem. Pushing past that pain is a learned behavior. [M. Scott Peck, The Road Less Traveled.]
My hunch is that, at best, it will take more than a modest increase in hours work to move from "delivering whenever it is ready" to "delivering on schedule". This leads to the problem that, whatever you try, if people didn't really buy into it, the one thing they will know at the end is that "it didn't work".
Sorry to give you a hard time on this. I know it is a tough problem, and I wish I could be more constructive. I'm glad I'm not a manager.