I think you're going to run into a few issues trying with that plan.
The first is trying to find a Ph.D. program that starts in the spring. They are rare.
The second is that if you do find a Ph.D. program for the spring, you are going in knowing that despite being granted full funding by the university, you are planning to leave at the end of one semester.
Also, when applying to schools from the fall, if you do not tell them about the program you are currently in, you run the risk of having to retake the courses anyway.
If you tell them about the program you are currently in, the schools may view you the type who would leave if you found a better opportunity.
I would recommend that you try to take graduate level courses at your big state school (where it will be much cheaper) as a non degree student, while working or earning grants to support yourself.
Then, when it comes time to apply to programs for the following fall, you can show them that you are motivated to start your Ph.D., that you (presumably) did well in graduate courses, and are not withholding any information from them.