You have discovered the one thing “wrong” with spruce. You have to sand the tapers on.
There is an expensive taper sander that runs about $170 but is the top-o-the-line answer to it. Or there is the $10 answer that requires some work on your part. Both are available from 3Rivers.
The $10 answer is a board that has a groove cut in for both the nock and point taper angles. You use it in conjunction with a sander.
I bought one and rigged it up to use with my belt sander. My sander table is hard to clamp things to so it didn’t work really well for me. After I committed to wood arrows I just bought the expensive taper sander.
But if you have some time it wouldn’t be that hard to build a jig to make the $10 option work either.