"your contention that temps during that time interval have a constant value of zero"
If you are trying to say that there has been no change in global temps in that time interval, then that is your premise. If have merely stated it more clearly to facilitate testing and understanding of what it is that is being tested.
It seems to me that you are grasping at straws here. Cherry-picking the time frame by shifting it three months forward will barely affect the numbers at all. Data from the first ten months of 2012 show it to be warmer than the average for 1997-2011, suggesting that 2012 will be the fourth or fifth hottest year on record. That will increase the slope of the line, weakening your contention even further. A better idea that gets us around the calculation problem is to wait until the December figures are published, then run the calculations using 1997 through 2012. Much easier to calculate and also more indicative of what is really happening.
Also, there is no straight line slope in the surface data. That means that at least once, the trend was NOT zero. And that means that the rate of temperature change changed during the 1997-2011 period. Shifting the reference period slightly will not have much effect as the F-values are nowhere near the critical values.