You have my deepest sympathies.....
I've been trying to do that same thing, since the first day that I installed Windows 8.1. (it's been a while)
So, not being able to put my favorite internet shortcuts in my task-bar, I put them in a folder on my desktop. I number them according to their importance. Like:
1 Windows 8 Forum
2 Windows 10 Forum
3 Kia Soul Forum
I can also minimize that folder to the task-bar.
I usually leave that folder open all day, but I try to make it as small as possible so it only shows the names and not all the peripheral BS. I actually have two folders, because I work too many forums to fit in just one folder/window.
If memory serves, I've not been able to directly copy an Internet Shortcut to the Task-bar, since Windows XP.
I guess that's one of those "Improvements" that we're suppose to embrace. Eh?
Computer Type PC/Desktop System Manufacturer/Model Number Gigabyte OS Win-8.1 CPU AMD 8 Core Motherboard Gigabyte Memory PNY, 4GB Graphics Card NVIDIA, GForce 210 Monitor(s) Displays 21" HP
Keyboard HP Professional Mouse GearHead Wireless PSU Antec Earthwatts, 650 Case Pac-Man Case Hard Drives Seagate SATA III, 500GB Internet Speed 5 Meg Browser Firefox Antivirus AVG Free Other Info Using Classic Shell on Win-8.1 pro