How much away is she from the cut off? You may want to ask if they would put her in the 3 year old classroom once she turns 3. I've seen such cases.
I think advanced placement in preschool is unusual and you may be the first person ever asking about this. I am not that surprised that the teachers/directors were taken back by your question. I don't know where you live but our state mandates teacher:student ratio based on the age. The ratio is different for 2 and 3 year olds. This itself may make it very difficult to accept younger child.
The question is what you want for her. If it's an academical stimulation, workbooks and such, it may not work anyway if she is gt. Lots of people on this board (me included) were happy with a play based programs which did as little academics as possible. You may look into Montessori and see if they would accepted her. We tried that with our younger one and it was a wrong choice for him.
If your goal is for her to be around other kids then you may have easier time finding a program for her. Some drop of programs start at 3 and it may not have to be necessarily preschool, she may be happy to take an art or gymnastics class. You may also want to look into multi-age classrooms which may be eventually a better fit for her if not this year than the next one.
Is there a school where 2 and 3 year olds spend lots of time together? That too could be an option.
