What should I set the DC at for leveling up via a test?

Hello! I'm planning to DM a new campaign, and I have a funky idea that I want to try. It's going to be in a school setting, and I really want to do something specific for leveling up. Basically, Strixhaven: A Curriculum of Chaos introduces exam-taking as a mechanic. For those unaware: you roll two ability checks. If you fail both, you fail the test. If you pass one but fail the other, you pass the test. If you pass both, you ace the test. There are also ways to study for the quiz beforehand and get the chance to reroll failed checks a limited number of times.

I want my players to take exams in order to level up. My plan is this:

1: The story of the campaign will take place over the course of a calendar year, so 12 months.

2: Players' maximum level may not exceed the month of the campaign (so, if we're five months into the story, they get to be level 5 but no higher)

3: Every Sunday, if players have the ability to, they may choose to take an exam to level up.

4: Failing the exam means that they are not allowed to level up that week, but may try again next Sunday.

5: Passing the exam means that they may level up as normal.

6: Acing the exam means that they may reroll their new hit die at advantage when determining how many new hit points they get.

So, here's the problem: I need to make sure I set DCs that make this system challenging but rewarding. It won't be that interesting if players ace the exam every single time, right?

What system should I use to set the exam DCs for each level-up?

I've playtested a version of this where the exam DC was always "10 + (<the level you are trying to reach> / 2, rounded down)". So the exam DC to level up to, say, level 6 would be 13. Under this version of the system, my playtest PCs aced almost every exam, with only 3 on average being passed without acing. That feels too easy to me, but correct me if you disagree.

My other thought would be making the DC = to 10 plus the level you're trying to reach, but that would mean that the final level DC is all the way at 22, which I'm not sure if that's going to be too hard or not. What do you think?

Another problem I'm noticing: it's actually better to fail an exam than to pass without acing, because then you get another chance to ace it next week, whereas with passing, you're just stuck with a chance to get less hit points on your level up. That doesn't feel right to me. Any idea how to improve this?

Last thing I've noticed: Rogues and Bards end up being unusually tanky under this system, since they get bonuses to skills. But quite frankly, I feel like that's kind of a feature, not a bug. Do you think that's okay?