Just start anew. It's obvious from the picture the wires are under stress. The whole cable will be more stiff than if the individual wires are not twisted. Just take your time and carefully twist the wires together so they have no stress in them. As FraGGler said, the wires will let you know if they like it or not.
"twisting" wires is a misleading term. We really bend them around each others. Take a look at this video, which shows a machine that makes wire rope out of individual steel wires:
On the large rotary machine is mounted all the spools containing the wires. If you pay attention, you will notice that as the machine spins, the individual spools always stays in the same orientation. They stay horizontal. This is done so that the individual wires are not twisted. Wires are like springs, if you twist them they will store energy and stay under stress. It makes the whole cable less flexible, more prone to failure and more dangerous when it fails.
The same technique is used by cable manufacturers to make electrical cables.
Perfect, thanks! It was definitely the tension that was causing a problem. I just did it by hand and it turned out great. I spent hours on the litz braid and skimped out on the twisted pairs...
Not sure how the guy on youtube got such a perfect twist with his drill though.