I think you first need to assess whether your policies can be reasonably followed. Why do you need to spend so much time and effort on teaching the policies to begin with? What are the barriers you and your people are facing that make it difficult to follow these policies and how can you remove them?
Ideally, the company environment should be such that following policies is the default action, with little to no conscious effort. The policies and the environment should be such that it takes effort to not follow policies. Workers shouldn't have to have a list of rules memorized in order to be able to do their jobs.
It's the manager's job to make sure following policies is the default. If it's not, then they need to seriously consider either working to change the policy (bad policies), change the environment so that the policy can be followed (good or unchangeable policies), or provide a compelling and logical reason to your team why the policy and environment cannot be changed and concerted effort is required to follow the policy in question (unchangeable policies). As a non-manager, it's your job to make sure management is aware of policies that are difficult or impossible to follow and what the barriers are.
In the cases of policies that are staying, but need environment change, communicate the current expectations and a roadmap of the environment change to improve compliance. Get feedback on how and why a policy cannot be followed (or why compliance is low) and engage your team to solve the problem. (As a non-manager, work with your manager to obtain and pass on this information.)
Developers, especially, don't like rules for the sake of rules, and forcing rote memorization and blind acceptance is going to end in disaster for your team. Your planned attempts will only result in a disengaged team at best.
Instead, harness your team. Developers are problem solvers by nature. Explain to them the problems with compliance that management is having/seeing and ask them for help solving it. Ask them why they can't/won't comply with the policies and work with them to find solutions and middle grounds. As a peer, you can include your own thoughts to pass on to your manager and be the advocate for change.
ETA You stated that you are the peer of the people you are tasked with teaching. So I have to ask: why are you being held responsible for this, as opposed to your management chain? This sounds like something that a manager or team lead should be responsible for carrying out, not a peer.
If you are in a position of authority (either formally as a Senior or Lead, or informally as a highly-respected member of the team), then most of my recommendations still apply, though you may need to petition your management to enact environment and policy changes. If you are not, then I suspect your company has more issues, because unless you're considered a leader, your coworkers don't really have any incentive to listen to you and may in fact come to resent you for trying to do this in a dictatorial or "teacher"-like manner (due to the rather artificial authority).
In other words, it sounds to me like there are managerial issues that need addressed and my recommendation is to ask questions of your management for this, instead of blindly trying to do what they say. By asking you to do this, I believe they are barking up the wrong tree, so to speak.
You don't have to be a manager to question bad policies/decisions, to advocate for improving your work environment, and to hold your managers responsible for what they need to do.