I want to make a pullover jacket for ice climbing, and I'm looking for a fabric that is similar to the fabric used in the Patagonia Ascensionist.

Anyone know of a similar fabric that I could get from Seattle Fabrics, Owfinc, or another like online store?

No first hand experience but based off the backcountry.com user reviews found at:
http://www.backcountry.com/patagonia-ascensionist-softshell-jacket-mens

one user says, "The Ascensionist is thick polyester coated with Deluge DWR for wind and weather protection as well as water resistance. The result is a fabric slightly heavier than the Schoeller Dryskin(which I have borrowed for a day of skiing, and also found it to be a bit breezy), which would provide more insulation against air movement. It would be comparable to the Polartec Powershield (I have used both) and I don't believe there is a tangible difference in practicality for either fabric. One thing to consider may be the new Powershield Pro fabric introduced at the Outdoor Retailer's Trade show this year which may be an impressive leap forward in weather resistant soft shell fabrics."

Polartec powershield is expensive but can be found at seattle fabrics.

I did a quick google before I posted this and found that too. I think there are different kinds of powershield, but I made a pair of ice climbing pants out of powershield from OWFINC and found it to be very different from the ascensionist fabric, so I was kind of surprised by that comment.

Anyone have any experience with Schoeller dry skin?

i believe that schoeller dry skin or a similar weave softshell fabric may the the closest youll get

the patagucci should be a non membrane weave fabric

The REI Acme pants are schoeller dry skin (again there are a few different weights of the material). The pants are good enough feeling in the store and dryskin has such a great reputation that I'm picking a pair up for myself.

So if you want to try some out your local REI may be a good place to get a feel for dryskin. From everything I've read, no one complains about the fabric.

My recollection of the Ascensionist (and ReadyMix before it) is that the fabric is very tightly woven; much more so that Dryskin. It's also thinner, with a much lighter 'fluff' on the inner face, again, compared to Dryskin.

The ReadyMix/Ascensionist are, IMHO, very robust windshells, trading insulation for air permeability. Dryskin offers more a little more static insulation, but is more air permeable. Pick to suit your operating point...