OK here it is - the short version first:
Yes, I think the Auditorium A23 turntable platter mat sounds better on the WTA than the stock mat.
For the whole story and what "better" means in this context please keep reading.
System Description:
I've owned my WTA for about 5 months and use a London Decca Super Gold cartridge with it. This feeds a highly modified EAR 834P phono stage. Control unit is a DIY HiFi Django AVC using Silk autoformers. Speakers are Hawthorne Audio Sterling Silver Trios - a high quality custom made open baffle design. Modded Quicksilver Mini-Mite Mono amps power the 15" coaxial main drivers. A passive R/C filter is built into the amp inputs that rolls off below 100Hz. The signal is also fed to a rebuilt Dahlquist DQ-LP1 electronic crossover set for 100Hz turnover and then to an ATI 1502 amplifier which powers the two 15" Augie bass drivers in each channel. Speaker cables and interconnects are made from Clairvoyant Cable wire and are of my own design. AC supplied via two 20 amp dedicated lines.
Methodology:
When I got the A23 mat last Monday (7 days ago) I marked the WTA arm pillar and damping well for their stock settings. I also placed a small tubular level here, put the arm on a standard LP, took a picture, printed it and kept it next to the WTA for reference:
This allowed me a second way to visually verify VTA for repeatability. (the level was better centered during the trials).
I listened to the A23 for about 3 days with no changes other than set-up in an effort to "get a handle" on its sonic signature. I then proceeded to do A/B of the stock mat and A23 first with extended sessions of each. For the last 2 days the sessions were for one or two songs from albums I know well and use as references. Changing the mats and the necessary parameters took about 2-3 minutes.
What I heard:
Interestingly these 2 mats sound a lot like they look.
The stock mat sounds very, very good as you WTA owners well know. It does lend an "airiness" to the sound - like the instruments are floating on a pillow of air. Instrument images are a little diffuse and not totally resolved in contrast to the A23. Compared to the A23 it also sounds a bit rounded in its tone. Transients are not as sharply reproduced which is what I feel may cause this "roundness." In all this a quite pleasing sound and makes the stock mat very easy to listen to and a bit forgiving of less than stellar recordings. There is a euphony to the sound of the stock foam mat, though it does not give "the last word" as to all of what is on the record.
The A23 mat is about 1mm thick and as has been previously stated it is constructed of a very dense fabric type material that would be at home as a high quality convertible automobile top. It is flat, smooth and woven looking on one side and lightly textured in a cross-hatch pattern on the other. I would guess that this side is applied in some way to the other and that there are two layers to this mat.
The mat arrived in a too small box (more on this later) which contained only the mat - no instructions, product info etc. So my first job was to decide which way was up, literally! A brief A/B of the two sides told me that textured side up was the way to go. This was confirmed shortly thereafter in via email with the supplier.
The A23 provides a more direct connection of the record to the platter. The first thing I noticed was better transient attack to notes and this improved tracking of transient information may well account for much if not all of the improvements I hear with the A23. Plucked strings of guitar and harp had more of the sharpness of nail on the strings. On other instruments and vocals this was shown as a more true timbre and ultimately a more "real" sound. Images of individual instruments have a solidity that is different than that of the stock mat. There is more dynamic impact with the A23 and I'll even go as far as saying that overall dynamic range is also enhanced. The sound stage expanse is similar to that of the stock mat but the "airiness" is not the same. Still this is a very musical sound. It is not at all dry sounding and I get the sense it is giving more of what is actually on the record.
If I had to use only one word to describe the sound of the A23 mat I would choose VIVID. Recordings have more resolution, definition and apparent dynamics when using the A23 mat. This is why I deem the A23 "better" than the stock mat and for me it is a keeper. 
My Decca cartridge is the most live and lively sounding cartridge I've yet encountered. With the A23 mat it sometimes walks a fine line between high resolution of a recording and too much of a good thing. Fortunately the vast majority of what I've listened to so far sounds great.
I can imagine that if a system is having problems particularly in the high frequencies the A23 could possibly push things over the edge.
Disclaimer: This review describes my experience with the A23 mat in my system, in my room, with my ears and my preferences. I do think that much of what I've heard and reported is generally transferable to other systems. But,, you know the old YMMV caveat.
*** I spoke with Matt Rotunda of Pitch Perfect Audio about the way the mat was shipped and was informed that it was in the same unopened box as received from the distributor. The mat was in a soft half fold to fit into that box which caused a slight "ripple" to take a set in it which has yet to completely relax. However, the weight of an LP does flatten the mat with no problem noted. I suggested that an LP sleeve/mailer combination would be better suited. Matt said that he'd relay that info to the distributor.
