I was thinking you could make a 15 degree cut on all 4 sides of the ends of each spindle.
On a piece cut to the width of the spindle, make 15 degree end cuts on multiple pieces, each the exact width of the spacing you want between spindles. Tack and glue in place between spindles.
Take long pieces of thin trim and make a 15 degree cut along one edge. Pin and glue along the length of the top and bottom rail to lock the pickets in place.
You'd need a jig to hold the pickets vertically with the ends against the bit. If there are differences in the sizes of the ends of spindle, you'd need to do some sanding or hand plane work, or find a single source all the same size.
The more I do, the less I accomplish.