I have a '59 Kodiak, and one from the '60's (I don't know what year). Both are 45# @ 28, and I draw 28". The '60's Kodiak didn't have a string, so I made a Dacron string for it, and it always shot where I looked with 3555 GT and 125 grain point. The '59 had a string with it, and it always shot to the left with 3555 and 125 grain point. Finally I decided to make a new string for it out of Dacron, and now it shoots where I look with 3555 GT and a 145 grain point.
So my experience is that you are not overspined, if anything, the opposite. But you may have better luck with the new Dacron string you've ordered.