Apple doesn't make a different base so you will need to look for a 3rd party option.
I have a very similar situation where I need to see over the Cinema Display (to watch the television across the room) but the height with the supplied base was too high. After looking all over for a desk mounted arm that could support the weight of the display (~23 pounds) I went with the Ergotron Mx Desk Mount arm (Amazon.com for $114 or AppleStore from $169). Many of the other arms, including Ergotron's lineup, have more joints or features but the Mx is one of the only models that could support the weight without costing twice as much. Ergotron also has the Lx model that says it supports up to 20 pounds that you might like instead of the Mx. The 23.5 pounds of the display includes the weight of the base so without it, you are very close to the 20 pound limit of the Lx arm.
(Note: as with most of the display mounts, it is a VESA standard connection plate so you will also need the Apple VESA mount adapter to connect it to your display).
With that connected, I can lower the display all the way down to the desk (although I keep it about 1/2 inch up for the speakers and for airflow intake) and I can just see over the screen. A movable arm also has the benefit of when I don't need to see across the room, I adjust it up higher for a more comfortable viewing position. (Putting the top menu bar at eye-level is the recommended height)
Also, if I need to show something to someone sitting a way from me, I don't have to ask them to come over but can just lift and turn the screen around to show them. Normally this would not be very easy to do with a 27" and 23 pound display but the Ergotron arm makes this effortless.
I do this often during parties with the music playing and an iTunes visualizer or cover art show is on the display. I get a lot of "Oh, now THAT is cool! Honey, can I get one of these?" responses when I do it.
and if you go with an adjustable arm mount like this one, be aware that the default tension will not hold the display up so don't let it drop on your desk. You will most likely need to loosen the tension just to attach it but then tighten it until it can hold the display up in a floating position.
Here is a video on YouTube I just found in another thread showing someone disconnecting the Apple base and connecting a VESA adapter and Ergotron Lx model arm to a 24" display but the procedure is exactly the same for the 27". Although the instructions in the VESA adapter package is very detailed, a video with someone explaining it always helps too.
Hope this helps.
Just a side note, the only con I have with the Mx is that I can't lower it any more. I would like to tilt it back at more of an angle and lower it even futher so I can see over it better to see stuff lower on the other side. The Mx arm tilts back enough but then doesn't lower that far down. It is like it was made with the 27" display in mind as it lowers just down to the desk. Some day I'll either try the Lx and see if it can adjust to that level or perhaps buy a new flat panel television and mount it on the wall high enough so that I don't need to adjust my cinema display. Hrm..... You know, I think I'll have to go TV shopping soon .
Oh, something I just remembered about the Mx model is that the vertical height limitation will not allow you to mount the 27" display in a vertical portrait position and adjust it. I could put it in this position but it would be right at the desk.
I believe the Lx model would have the height to do this but I'm not sure. The older Lx model had a 14" desk pole but the current model is about half that pole length.
I went with the Ergotron Mx Desk Mount arm (Amazon.com for $114 or AppleStore from $169). Many of the other arms, including Ergotron's lineup, have more joints or features but the Mx is one of the only models that could support the weight without costing twice as much.
Thank you so much for your very helpful response. Much appreciated. I went and had a look at the suggested product, but one additional limitation I have is a that my desk is not very deep. So I had a look at the Ergotron site and found this product. It's a simpler product, but perfect for me. I've asked somebody to hunt it down for me here in Bangkok, so here's hopin!