show progress so your management can see what you are doing. They have no idea if their decrees/wishes are reasonable. I don’t think there’s much point in fighting with them until you’ve accomplished half of the ranked backlog or worked through half of the schedule. Once you’ve done half of the backlog or half the schedule, now you have data and can see where you are.
Now you can take your data, and use the previous option and provide estimates for the rest of the backlog with confidence ranges.
When I’ve been the project manager for imposed dates and imposed backlogs, I’ve explained to management that we will do our best, but that we will maintain a reasonable pace from the beginning and when we are halfway through the time and the backlog I will report back to management where we are. Did they want to know where we are a quarter of the way instead, where we have more flexibility?
That changes the conversation. Sometimes they do, and sometimes they don’t. It depends on crazed the management is. I also protect the team from multitasking (none allowed). I am the Wall Around the Team, protecting the team from Management Mayhem.