Some brush-script types have the effect of the strokes tapering in, thickening, then tapering out, e.g. Duffy Script.
(Sorry to keep plugging my own fonts, but for some reason they come to mind most readily!)

There are various means to “abstracting” a typeface. I wouldn’t say Trajan is a good example of it.
As a point of interest, it seems that Brancusi is Adrian Frutiger’s favourite artist: http://typophile.com/node/86653#comment-495529

Maybe some of those futuristic faces with semi-incomplete letterforms can get you closer to that sangreal. Maybe that very (in)famous Stop.

I would have thought : Futura

Condor or one from the Aviano series?

You are thinking about the R leg i Trajan, right? There are plenty of faces with such details. Quadraat, Fedra and Bembo off the top of my mind.

With such a slender shape I would also look at thin stressed sans serifs like SangBleu BP Sans.

There’s something about that terminal that cuts off the curve that you might find echoed in other faces. What are you going to use it for?

Yep, Indra is on to the same lead, but IMO they both look too strict and geometric next to the sculpture.

I would look towards Excoffon.

hhp

Another option could be something like those suggested here:
http://typophile.com/node/83125
Or this:
http://typophile.com/node/82518

Thanks for mentioning Noir, Riccardo. I left it out because it's so geometric.

Thank you to all,

WOW! this is more than I ever imagined. The ideas and discussion has ignited an explosion of alternate ideas that had never occurred to me.

These are all great suggestions... Duffy Script, Frutiger, Stop, Futura, Condor, Aviano, Quadraat, Fedra and Bembo, SangBleu BP Sans, Excoffon, Typonine Stencil Pro, Dala Floda, Noir.

I will have to start working with them and see where it leads me.

Side notes:

To Frode Frank, I'm redesigning a logo that has a bad stylization of a bird and has Helvetica Bold for the company name. The concept of a bird is the only part of the logo that has a connection to the mission of the company. I plan to redesign the bird and match that to a appropriate font. I am so grateful for the font suggestions.

I appreciated the link from Riccardo to the comment by William Berkson about Frutiger. I've always liked Frutiger and obviously Brancusi's sculptures. It is interesting to know the link between the two.

Also, Thank you to Riccardo for making me aware of Noir. The font is too geometric for what I'm working on now, but I was impressed with details of the font and the font defiantly has echos of Brancusi's sculptures. I'm not clear if Noir is complete but when it is complete I want to purchase it.

Thank you again.

Warmly,

Bill

You can contact me offline about Noir (I'm the designer) if you are interested. For your logo, why not draw something from scratch?