The wire will fit 3 times with the nylon coating. Do it all the time. But I will admit it can be a trick. The end of the crimps are often crushed/deformed, I assume when they cut them to lenght. You often need to slightly flare the ends. It also helps a lot to cut the end of the pull-pull cable on a bevel, such that the tip comes to a point. It feeds better that way. Work the cable in slowly. Only try to push in 1/4" or less at a time. Sometimes needle nose pliers help to grab and push the cable. Once you have the tip thru, it is easy to pull the remaining cable.

Cheers.