Get ready for some fun. That's my advice! Ok- here's what I know...
I've spliced some tough, used 16-strands. Never has it been impossible, never has it been easy.
You have a long tail before the taper starts. What is it? 28" to the first mark? Make that a LOT longer. Make it 38" or more. Don't be cheap here. Now here's what you do: Look at that tail, you have a tail several feet long. If you made the first mark at 38", then start pulling out strands to make the taper, the tail gets thinner AND longer. So you might have 50" of tail. Don't worry, you'll need it.
Now proceed with the rest of the splice, marking here and there, pulling out the core, etc....You'll get to the point where you are going to do the cross-over bury...the toughest part of the 16-strand splice that NOW will be WAYYYY tougher because the rope is old, stiff, and tight.
Before connecting that super long tail to the wand/coat-hanger, go up about a foot or a foot and a half. Put a mark there. Let call that the super-taper mark. Starting at the super-taper mark, grab on or two of the strands and cut HALF of the threads that make up that strand. Do not cut all the way through a strand here. You should have 6 strands that make up the tail. You want to have six when you finish this super taper. So you cut half of one or two of the strands. Now go maybe 4" towards the tip of the tail and thin out 1 or 2 of the other strands. Now go down and do the next.
Here's where things get fun. These strands are gonna be wacky. They'll start fraying and they'll just be outta control. Starting at that super-taper mark, start braiding the six strands together (in pairs, braid it doing a standard 3 strand braid that girls often do to their hair). Braid it nice and tight. The goal here is to make a thin tapered tail that will be a breeze to bury in the cross over, then you'll use this tail to pull everything else through. So after you braid the super-taper, go back and snip off any loose ends sticking out of the super-taper....just to make it super-smooth.
Now you're ready to rock and roll. Pull that super taper through, then anchor it to something and pull on the rope and the super-taper will pull the regular tapered tail through (eventually).
Now you'll get so that the normal taper of the splice is maybe half-way buried. This is where things get totally insane. ....Ok, just kidding. I guess I was getting a little excited. You just have to work the rope. Don't try to bury it all at once. Bury a little. Just because you COULD go more, doesn't mean that you should. Bury a little, milk, massage, then bury a little more.
Keep this up for a while. Don't be ashamed to use some KY (yes, splicers should have some of this on hand...er ...uh....available for .....uh....) Ok, honestly, a water-based lube will make things go smoother if you're really in trouble.
There might be little tips here and there that'll help. I don't think it's necessary to wash the rope first. I've never done it. Though I guess you could wash with a fabric softener to soften things up first, but I haven't found that to be necessary yet.
If all else fails, you could also send it to someone who would be willing to do it for you.
So what rope are you splicing?
love
nick