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Dudley,
At the old tratan27owners.com someone with a user name of CStroup posted a photo of the centerboard aligned over a 1" grid. I am attempting to contact him to see if he can find this picture. Alternatively Ken may be able to find this photo but I would not be too hopeful of that as it was embedded in the Projects section of the old forum which has not been recovered.
Tartanparts.com will graciously sell you a replacement for $1200 that takes 4-6 weeks for delivery. You might be able to talk to them and see if they will 'give' you the exact dimensions. I am going out on a limb here but I bet that you could get this made by a local metal working shop for well less than half of what they want. I can only assume that your old C/B is gone to the bottom of the ocean so you can't get the dimensions from it.
On a related note I was finally able to paint our centerboard this spring after 4 years of ownership. I was surprised that it was in pretty good shape minus a ton of barnacle buildup (even in the lower Hudson River). It is pretty rectangular so it should be easy for a metal shop to fabricate. I could not tell if it was epoxied or just a metal that appeared to be at least 1" thick. The information.htm File on T27Owners says that the early models had a bronze centerboard as you already seem to know. I think that it weighs over 100#s. Not sure if this helps.
Alternatively you might be able to get the exact dimensions from Sparkman & Stephens website as Olin Stephens was the designer of this boat. I believe that there is a link to S&S under the Links section.
You can sail the boat without the centerboard but I would recommend you get a new one made as it adds ballast down low and helps the boat tack upwind among many other useful attributes that includes steering under power in tight spots.
Good luck with this. We will try to help out as we can.

Caleb
#328 Odalisque