Jim, Jamie said the right answer. Following the manufacturers directions is the answer. Have you done other double braid splices on easier to splice lines like Double Esterlon, Sta Set, or Stable Braid? These lines have a softer weave and come together easier, though they still present some challenge.
What I'm getting at here is that your difficulty might not be coming from the taper pattern. It is coming from one of two other things. There is a slight chance that the spool of rope your beeline came from was woven a little tighter at the factory and therefore is harder to splice. This is less likely, but the companies are always tweaking the rope recipes, so it is possible.
The other option I can see is that you haven't got all the nuances of double braid rope down, so when you get to beeline (which is a harder to splice rope as it is...compared to regular double braid) it sorta locks up on you. The quick bullet points i can share are:
1- Stitch the crossover together to shrink it a little
2- Keep tension on the eye while running it home. Especially keep tension on the crossover side
3- Before the burying gets difficult...BEFORE that point, stop burying and firmly bend and massage the rope and it's stiffest point. This brings up slack from further down the rope and puts it where you need it. Do this for a good 2 or 3 minutes. Bend sharply.
4- I rarely do this one, but a mallet can be used to soften up the hard parts
5- In extreme cases you might have to apply some Astroglide to allow things to move better. No joke. I only do this one maybe once or twice a year
6- Put a large fid in the eye to give you something to hold onto
7- Pull with one hand, milk with the other...at the same time
8- On that last inch of the bury switch from pulling and milking to just simply shock loading the splice (by hand)
9- I don't think pulley setups are ever necessary to bury a splice, but some people use them with success
10- Heavier people are better at the running home part of the double braid splice. I'm not very heavy, so there is less heft on the line. I've found that 2 people working together, one pulling, one milking, can bury even the toughest double braid splices.
Other than that, make sure your measurements are all lined up right.
Bluemoon (aka Poison Ivy, aka 11.7mm Blaze) is even harder to splice.
I'm sure there are a ton of other tips and pointers that I'm forgetting. This is just what I thought of sitting here.
Let us know the specifics problems you are facing and we can help you address those issues. Post up lots of pics and have fun!