I had one that confounded me exhibiting similar characteristics to the one you describe and found that there was too much side to side play in the trigger. After adjustment this allowed the trigger to trip in the manner you describe. After carefully squeezing the area where the trigger pin goes through and removing the play I was able to adjust it into a fine trigger using the adjustment procedure found here http://www.varminthunters.com/tech/savage/ without any stoning. You may also try shimming it with some tiny washers to eliminate the side to side play if it is found to have the same problem I experienced.
I hope this helps
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