This is typical of the stain/poly mixes. They also don't have the depth and clarity you will get with a stain and top coat process. If you want high quality finishes you can't short cut the process. I never use them and don't ever recommend them to anyone.

Can you tape the bottom where the two pieces meet so there isn't excess stain on the board? Also, try wiping the spindle with lacquer thinner and then immediately apply the stain, spindle by spindle. Often soft woods such as pine will streak, even with preconditioning.

Thanks for the help. I've decided to use separate stain and topcoat.