You probably would want a June UY.
Don't confuse the banking deadline with the dates they expire. You mentioned a spring UY but mentioned they expire in the winer. They would expire in the spring.
With a June UY, you have until the end of the following January to bank them.
Once banked, they would have to be used by May 31st of the following UY.
Example:
You have June 2008 points. You don't use them all in 2008. Prior to the end of January 2009 you bank them into your 2009 use year. These banked points then would be good then through May 31, 2010, expiring June 1, 2010.