I stand in ore that you are willing to tackle such a problem. On a sampling course involving Gy’ s Theory the suggestion was to distribute the material evenly – therefore use a flat area and distribute the material evenly say to one meters depth. The problem with this was

Finding enough room and
In your case the size variation.

Is there some way to reduce the size variation to a more manageable rang? Sadly, other than that I would find myself reverting to your original method.

Our company has developed software which evaluates grade and tonnages from your metallurgical process data knowledge. http://is.gd/yvKP6W After I asked my colleagues, they said it is almost impossible to obtain a representative sample from a stockpile and that you are correct in saying you are better reprocessing it – to obtain a representative sample from a stream of material, rather than a stockpile.

There is a way to take representative samples from stockpiles; sonic drilling in combination with the patented aqualock sampler. This technology takes rapidly highly undisturbed samples with a core recovery of 95% >

Where other techniques fail due to the difficult to sample stocked ore / minerals, this will be easily doable with sonic. More and more mines in the world are using this technology to determine their stock piles.

We are here playing with one of the cornerstones in sampling issue: it may be cheaper to "just do it" than to spend lots of thought on how to reliably sample (i.e. take a small fraction of the real thing that will return testing results reasonably similar to those on the whole lot).

I read similar conclusions about WEEE composition: the best available analytical device is the mass balance of an actual processing facility (Morf and others, Waste Management 27 (2007) 1306–1316; see also Waste Management 28 (2008) 1100–1112)
Yes, reprocessing is often correct.

We did a work at mine in North of Chile, and the only way to do the work, was look for all the information available, such a mining report, ore control report, topography, etc., and reconstruct the history of the stock, 3 operational stocks. The work was made in 3 month, for last 6 years of production, and was satisfactory and the result was compared with continuous feed to the plant.

You're literally between a rock and a hard place. I concur with the comment "so far have concluded the only way to find out the amount of metal contained in the pile is to run the whole thing through the process plant" - it's obviously the only certain way. However, I am also aware that the wrong decision here can cost many millions of dollars one way or the other. I am reminded of Terry Allen's tongue-in-cheek comment (""Two words of advice") in relation to sampling in such scenarios "Don't" and "Never". In a practical sense though you have a heterogeneous system with substantial nugget effect and segregation. You can predict minimum masses for sample sizes with Gy's and other theories and these minimum masses are likely to be many tonnes. Based on what you actually take you'll be able to calculate a very large FSE (50 - 500%) but this ignores the probably considerably larger delimitation and segregation variables. The simple minimum mass (Vezin, Reed, Richards) calculation for 128mm (12.8cm - not even a few 10's of cm) is 3131 metric tonnes. Double that 'diameter' and you'll have 8 times the minimum sample mass. Put that in an XRF.

Whatever you do short of reprocessing and using correct belt or slurry samplers will have inaccuracies. Take the company accountant with you when you try to sample the pile and convince them of the need for correct sampling equipment in the first place.