You will massively improve your chances of successfully making changes in your workplace if you implement a simple and essential change first, then look to incorporate the more challenging elements later. In essence, "Start, then strengthen".
The temptation when assessing the scope of proposed changes is to correct all the known issues (major and minor) in the first iteration. Your thinking may be "I'm going to have spend a lot of time and energy convincing stakeholders to buy into these changes, it makes sense to try and fix everything as part of this project".
Before going down that path however, I advise you to consider the following:
1) Larger more complex projects/changes have more elements for detractors to criticise
2) "Minor" changes may cost more and extend the duration of your project more than you first expect
3) The business world changes very rapidly; the changes resulting from longer projects may no longer be relevant once they have actually been implemented, or worse, you could lose funding partway through your project and be unable to fully implement any of your desired changes.
My recommendation therefore is to implement changes in a series of phases/projects. Start with the most crucial items and manage the scope very carefully. Set up the project in such a way that you can build on it (future-proofing), but do not allow the scope to expand without first getting agreement from all stakeholders (i.e. scope creep). If possible, don't expand the scope at all...the goal is to keep things simple and fully implement the most crucial changes first.
My final piece of advice on this topic is to track the benefits of the implemented changes and to celebrate the results. You are then ready to reassess the situation and tackle the new essential changes (building on the project you've already implemented).
As always, I welcome your questions, comments and feedback.