So first of all, I would make sure that you know exactly how much Rice will cost. If CWRU’s aid was a different amount than what you expected, is it possible there may be some wrinkle in your situation that may complicate Rice’s aid as well? Do you have firm financial aid numbers from Rice?
You may be able to squeeze your degree into an even 4 years, even with the transfer. But… I will say that an extra semester isn’t necessarily a bad thing right now, if the cost isn’t too high. If the extra semester bumps you from spring graduation to mid-year graduation, that means you get a whole extra summer for internships, which might help with job hunting after you graduate. The job market is difficult right now for new grads, and every bit of extra experience could help. (If you are planning on grad school right after college, this might not be as relevant.)