I have never seen a Hawken tang that was shaped correctly. I first join the tang to the plug until I have a very tight fit, than solder the tang to the plug. Now I can turn the unit upsidedown, look along the length toward the tang to see if it is in line with the bore...they never are. I use three 3/8" steel pins in my bench vise to adjust the tang to get the small end in line with the bore. And I use heat of oxy-acetylene toch too get the tang's vertical profile to match the stock pattern's profile, being careful not to re-melt the solder. Then the tang can be inlet down the centre line of the wrist, the barrel channel already having been inlet.
Longrifles are a snap after you've done a Hawken. That long lolipop tang of a SMR is more akin to a Hawken tang.