Interesting solution how do you do this?
Normally tapered halyard is made from a full length rope where the cover is removed from part of the rope and the cover is spliced inside the core.
Have seen some experiments combining normal double braid with dyneema single braid - but don't think this i what the rope manufacturers recommend.
Good video of the tapering process
To strip a line use the same splice you linked. The only difference is that instead of burying the core right back where you extracted it, you first want to pull a leingth of core out of the cover. Basically instead of cutting off excess cover, you repurpose it as additional tail leingth.
For more detail (assuming a mainsail)...
Lets assume that you have a 50' run between the top sheave and where the halyard exits the mast, then an additional 20'' from the exit to the winch and lets say a 5' section for working.
Typically this would require a minimum of 125' of new line in order to make a new halyard. But since we are going to strip it, we will need significantly less line.
Since the only part that needs a core is the portion of the line is what will be carrying full loads, we really only need the 50' up the mast plus the 25' deck section. In addition we really want the cover and core in the 25' section that will fall on deck to protect the core where it hits all the deck hardware.
So our ideal halyard will be made up of three seperate sections.
1) A core only section that will be 50'
2) A cover and core section of 25'
3) a core only that needs to be 50'
To acomplish this we will need to buy 80' of line (a little overage to make splices in). Starting 2 foot from one end we are going to pull the core out of the cover like in your video. But instead of doing the taper immediately we are going to pull 50' of core out of the cover first, then finish the taper splice from the link (I also like to lockstitch the crossover to prevent slipping).
So from our purchase of 80' of endurabraid we have made up a high strength tapered halyard of 150'.