Okay, so I'm going to go more in depth on here on why I don't think the other logos work as well as Number 4 (and my response to 4)
Okay, this is coming from a designer's standpoint. I like logo 4 the best because it use a serif font, like your book. You want it to work with the book, since that came out first. However I don't like/understand the box and circle. I would just get rid of them because they do not have a purpose. The rest of it is good, the positioning of "Primal BluePrint" and how grok fits on the side.
One: if you have to make something gray in a black and white version of a logo, it usually looks not-so-good, that was my opinion of this one.
Two: I do like the san-serif font, however, I still stick to that the logo needs to be cohesive with the book. The circle outline thing looks awkward around grok. However, if you MUST go with a san serif, I would suggest this typeface.
Three was okay, but it's really static. I prefer four, as I said above.
I don't remember the numbers of the other ones, I just downloaded them on my computer.
The rest of them...the ones that have differing line weights don't work as well in the black and white versions, but I can see where the designer tried that because of the one that has same line weights. It doesn't look all that good either. As far as the other typefaces go, none of them work at all. If you're going to mix typefaces with a brand, especially serifs and san serifs, they need to work well together.
Meh, the more I look at number four...the more I kind of like the square and circle, even though they have no apparent purpose. I would still like to see it without those though. I guess I could just do it for myself, post it here for you to see and then your designer could do it the correct way since s/he has the original files :-D. Sorry for the ramble...
So I did make it without the circle/square.
I like it better with the circle and square because it gives it a sense of gravity. HOWEVER, that line is really thin and although it may look great on the web, print is a whole 'nother world. If you were going to reverse it (i.e. white on black) those lines would disappear, but it is up to you, Mark, on whether that matters.