Thanks everyone for the input. I made a quick spreadsheet using the formula provided in the Martin Sprocket and Gear document, and it seems to match various online calculators I have seen. For our application, it gives a center distance about 0.010" greater than Dr. Joes spreadsheet. Would this have been enough to take out the slack in our chain last year? I don't know, but I'm sure it would help.
My understanding is that the formula most people use is still an approximation.
This page here alludes to a more accurate method:
http://www.islandpondrailroad.com/chain.htm
It gives me a center spacing that is 0.015" greater. I know we are splitting hairs at this point, but I figure the more accurate the spacing, the less need we'll have for tensioners.