I think you may be stretching it a little there, but, you never know. I mean, maybe he chose take because he wanted himself to be reborn as Take-da of Sokaku fame, or maybe he just wanted to have aiki like his mentor (just joking there). Still, he must have made this word up from somewhere - it is not a standard word.
I fully agree. Personally I don't find a link between the two, but I was just trying to give an explanation to how someone could link musubi with the musu in Takemusu. As you say it is a non standard word and therefore we can only know the exact meaning if OSensei somewhere explained the name. It really doesn't make sense for us to guess on the meaning based on the characters alone, without finding support for our claims within the texts of OSensei.