If you start with 100 random time series and then select only those that match the recent instrument record, you no longer have a random selection of data. So why would there be reason to believe that they will consistently "cancel out" to a flat line?
If you ran this experiment numerous times I would expect to see the "average" line prior to the instrument record vary as a random walk.
If the series don't really correlate to temperature (and the red noise doesn't) even though they appear to during the calibration period, then how it moves before the calibration period will be random. So when you take your weighted average of this randomness they will tend to cancel out (or at least tend to be flatter than the reconstruction during the calibration period). The greater the number of series, the more pronounced the effect. The point being that a hockey stick shape is an artefact of the method used, whether or not the proxies actually are good indicators of past temperature. I am trying to keep this somewhat simplified.
Of course you don't have to take my word for all this, thanks to Climategate we have all the behind-the-scenes dirty laundry:
Just for funsies: a cousin comment to yours argues that the actual hockey stick issue is that they're no longer sticks if you extend them past 500 years ago. This doesn't jive at all with what your analysis would suggest: if there's no power above noise provided by the proxies, then wouldn't we expect the shafts to be infinitely long?
The reconstructions by proxy referred to by gd1 leads to a hockey stick as far as back as you can go. Expect of course were there is very sparse proxy data at which point the trends will be completely random.
The cousin refers to the obvious long-term temperature variability. Nobody doubts the major ice ages. But the long-term reconstructions use very different techniques.
If you ran this experiment numerous times I would expect to see the "average" line prior to the instrument record vary as a random walk.