Yeah, but the problem with going with the dojo with "better instruction" is, how does a beginner judge that? Obviously OP found things more to his liking at one dojo, but that was based on short acquaintance and no knowledge of aikido. With six weeks of training under his belt, who's to say he'd look at the two dojos today and see the same thing?
Here's another reason to avoid the contract: it's because OP is very unlikely to get his money's worth, i.e., a year's worth of training. I don't know OP or this dojo, but statistically, most beginners wash out before a year is up. It's just not possible to tell that martial arts training is right for you until you've had the training experience, and that means more than one class or even a short series. A lot of people will take an intro course and enjoy it, but when it sinks in that training = giving up several evenings a week, they find that they just can't sustain that commitment. Some people think that a contract will make them follow through, but it doesn't seem to work with gyms -- I don't know why it would work with a dojo either.
I am simply going on this person's description, which clearly identifies the better training atmosphere. Further, this person has six weeks to give it a try. If after six weeks this person cannot figure out whether or not to invest in that year, then I would be very surprised. I would do not advocate the contract system but can understand why some schools choose to do so. Typically most states do allow for withdrawal periods and a place would be hard pressed to justify no allowing for medical leaves. I frankly would be more comfortable with a month-to-month system, but to me the larger issue is the better training atmosphere. If you can somehow describe to me why you do not believe that this person is running a better dojo, then please share it with me. My mind is always open.