yokurk - go anyway that feels right. BUT, time is irrecoverable.
If you spend a month, a third of your available time, with nothing working, there will not be time available to "throw one away". The "throw one away" philosophy is about throwing something working away. It encourages engineers to get something that works, to act as a basis for learning and improvement. (I think this is often misunderstood)
Spending a month learning how not to do something is somewhat valuable. But my experience of colleges (I used to teach undergraduate and post graduate Computer Science and Software Engineering) is you don't get the best marks for discovering and quantifying an approach which fails.
On the other hand, if you have something that works in, say two-three weeks, then you have two and a half months to improve it. Think of this like an insurance policy; your chances of failure were significantly reduced.
Put bluntly, if you came to me asking for a job, and you said "I really wanted to do something original, but I couldn't get anything to work until the last 20% of project time". I'd ask "how does it stack up against a cheap, well understood, off-the shelf solution?" If you don't know, I would assume you are not an engineer. I don't hire people to "be original", I hire people to be better than anyone else. That takes a lot more skill and intelligence than just trying to be original. Any fool can be original, it takes talent to be better.
If instead you said "I wanted to do something original and better, so I built an off-the-shelf solution in a couple of weeks, tested it, found these inherent problems, fixed them, then built this much higher quality solution, which has these benefits (cheaper, fewer 'moving parts', simpler, more flexible, etc.) in the remaining 50% of the project time", then I'd be interested in hiring you.
I have helped design recruitment and interviews, and screen and hire lots of folks. I was responsible for training hundreds of university graduates every year to be software engineers.
One hard part of training was trying to get fresh graduates to understand that we needed better; merely different or novel doesn't matter if it is inferior. To do better they needed evidence, preferably based on reproducible measurement. Someone who happily spends months doing something 'original' without spending effort to properly understand what exists is not good to have around.
Fresh graduates who understood this were relatively rare. Many could talk a good game, but had no evidence that they could do it. This seems like a superb opportunity to stand head and shoulders above the crowd. Somone who takes a low risk, high success path is going to stand out.
Anyway, that's my $0.02
PS - I should add, an (amusing to me) observation is two-three weeks will be spent on exactly the same thing if the "being original" approach doesn't work. I.e. you'll still be making a ladyada-style shield and testing it. Also, if you were going to go the extra mile, and submit a superb, evidence based, piece of work, where you compare the performance of your original solution against an off the shelf approach, you'd also build it too.
I'd strongly recommend sketching out the "happy path", and "unhappy path" for 'submitting a superb project' use case. I think you will see things in a different light.
