Do one in the light and get a feel for it. Then try in the dark again.
I think if you keep trying, with a practice strip of film, in the dark, and then look in the light, you'll eventually get the feel for it, and you won't have problems after that. I'm not saying you won't get a "kiss mark" now and then, but once you get the feel of it down, you'll have it.
Are you pinching the sides of the film and then allowing it to naturally expand as it goes into the spaces?
I used to feel the film with my index finger in the center, as I pinched it slightly, with my thumb and middle finger, while checking now and them with my left thumb.
It sounds from what you described, that you are wrapping it too tight, most of the time. The film finds it's natural position as you turn the reel. You don't have to force it. Be gentle.
As you hold the film with your right hand and turn the reel with your left, it takes the film in, and it naturally finds the right place. If you are trying to fit it in, or push it into place, it's not going to work. Hardest part is the first couple of turns, getting it started tracking, where it's a smaller diameter, and less often the last couple turns.
Get the lead end stuck into the center of the reel, or even hooked, so it has an firm anchor in the center. Let the film pull itself into the reel. Keep checking after each turn or two. I have many rolls of film with the end having a hole, where I hooked it. That's why the center of the nikor reels has that sharp point. (at least they used to? It's been awhile) There's nothing you are losing on that half inch at the end.
If the lead end isn't tight, the film will slip and this will make it much harder to load.
35mm is easiest. I had more trouble with 120, because it flexed or twisted and wanted to jump the grooves.
Hope something in this, makes a difference and helps.
Like I started out writing. Once you get it, threading film onto the reel will be much more consistent. You just need to get the feel.
Honest, I have one old Ansco plastic reel and it was always more trouble because the film stuck and bunched up. Could be that I was just doing it wrong.
I hate to ask the obvious, but you are loading the film with the open end of the spiral face right, and turning the reel counter clockwise? If not, it will never work.