I realise this might be a bit late for your needs, but I thought I might write this for other people's benefit as well, now that I've seen the post.
I own a Zephyr, and one of my goals was to figure out a realistic and practical way to fly the Alexa. I'd done tons of research on these forums over the months leading up to my purchase of the rig, and the Alexa appears to be a contentious issue with the rig.
The Alexa is *perfectly flyable* (even with reasonable accys) on the Steadicam Zephyr *IF* certain conditions are met. I've (hopefully correctly) attached photos of two ways I have achieved the setup. Keep in mind that neither setups include accys (WFF, video link, matte-box etc.), BUT, the rig was still wide open for additional attachments.
The FIRST photo shows the camera body and lens mounted on top, with the camera taking 24v power from the two batteries I have mounted below. This configuration solves the weight and power issues. What you will need though is the correct 24v power cable for the camera (more on that in a moment), and it also requires the secondary, optional battery mount that Tiffen offers for the Zephyr and Archer2 rigs. Running the camera at 24v is essential in this case, as the 85w(minimum) the camera draws completely exceeds the amperage rating of the internal power cabling (Mark Schlicher has researched this extensively in one of his posts). The 24v cable is one that I came across on eBay. I took a risk with it, and it's worked fine so far thankfully - it seems to have been made with fine build quality.
The SECOND photo shows another scenario; I acquired a custom made, slimline adapter plate (THIRD photo) that eliminates perhaps half a kilogram of weight up top from the bulky dovetail plate otherwise required for a secure mounting. In fact, the payload was reduced to the point where I "had to" put a battery up top to get the gimbal close enough to the stage. You'll also see that I needed only the single battery down the bottom. In this configuration, adding WFF, video link, or anything else you'd reasonably throw at it is a perfectly viable option. Also, the camera now has it's own power, so sled voltage and current is no longer an issue for it.
Edited by Zoltan Jonas, 14 October 2013 - 07:21 AM.