I have been splicing the line you describe for years, but I don't use a conventional method. Here goes:
Make a loop the size you need. Lay the bitter end alongside the standing end.
Use whipping thread and needle and run the whipping thread through the center of both lines. Use several passes so that they do not move, and make the attachment point where the "Y" of the splice will be.
Then begin making a series of figure 8 loops around both lines. Make each loop very tight, and very close to its predecessor. Tight! I use gloves and a tool of some sort, like a screwdriver handle, to wrap my twine around so I can pull it tight.
Then finish your work just as you would as if you had whipped a line end.
My splices look neat and I have never had one fail.
When you come to a "Y" in the road, take it....Yogi Berra