I think you have the right answer staring at you in the face: what happens if you take the new project, fail your interviews and never get into MBB - what then? Will you hate yourself forever?
Having said that, I'd like to challenge two of your core assumptions however:
1. Do you truly need 2 weeks to get ready for an MBB interview when you arguable have already succeeded at such an interview at a Tier2 (even if the bar was lower, most of these do give case interviews). Let me answer for you: many of us got into MBB by preparing while working full time & having a family. Just commit to a plan such as "review feedback in the morning before work, listen to audio on my way to work, do a case in the evening and 2 each day during the week-end". Sure you will hate life even more than usual for these 2 weeks, but what's 2 weeks in the grand scheme of things?
2. You seem to believe this will be the last opportunity you have to apply for / interview at MBB. First, you can probably delay the interview if needed; second, they will probably still be interested in 6 months if they are interested today
Also, you mention that you've waited for "one year" to do this type of project? One year is NOTHING! I can't even remember the type of projects I used to dream of doing when I was 1 year out of school. [insert old geezer joke here]
Last but not least, let's also look at the bigger picture: You are just 1 year out of undergrad. Odds are, a Masters degree is in your future, which will then give you another solid chance at MBB.
Here's what I suggest:
1. If you are "MBB or bust", you take time off and prepare as best as you can
2. If you are a type-A and think you can do it all, you take this cool new project for now since it is important to you - but you also kick your prep into high gear before/after work and during week-ends; if you honestly feel you would need a little bit more time, ask MBB for a delay, they will usually try to accomodate. And you can still ask for a couple of days of beach time / PTO if needed (I'm sure you can be creative here).