Re: signing a contract
If you found a dojo where there is a good teacher, who is always teaching and is truly concerned about the students, then you have found your answer.
Almost all Aikido instructors are significantly underpaid for their services. Just look at what you pay for monthly dues at a good gym, your plumber, electrician, ..... I can understand that a good teacher would want to free up time by utilizing a third-party system that utilizes yearly contracts. In the grand scheme of what we pay during the course of a year for things such as vacations, movies, drinks at the local watering holes, I would think that the money for year at a good dojo in an excellent investment in your future.
I personally do not have a contract system and people pay monthly. I will let a person train for free for up to two weeks before deciding to sign-up as a regular student. I am not the cheapest or most expensive dojo in town. I teach about 98% of all classes taught. What my dojo brings in is like a hiccup to my "real" other full-time job. Good teachers teach their passion. Few if any, can ever retire, let alone live off of what the dojo brings in.
At the end of the day, Ushiro Sensei summed it up by saying that it is better spending three years searching for a good teacher rather than spending three years training with a mediocre teacher. You talked about one teacher being significantly better than the other. You get what you pay for (usually). Support the better instructor while investing in your future. The investment just so happens to come in a one year chunk.