Jeff,
I can see the faceting of curves in Sketchup as being a big issue. It is to me as well.
My background is mechanical engineering and I have used many different CAD systems over the years. All of them used true arc and circles so this was never an issue.
Of course they also had filleting (Corner Curves) which could easily solve your problem in one step. All could create a fillet between two lines, arc and line, or two arcs.
In your case it would be between the left arc and the horizontal line at the bottom right.
All that said I wonder about your need for accuracy in this case. In the real world everything has a tolerance and not suprisingly when you start to build things over 6 to 10 feet your measuring tools start to throw their own errors into the mix.
For instance how accruate do you think a tape measure is? Sag, flex, temperature, material and other factors add to the issue. This is why in building construction an error of 1/8 inch is an everyday occurance.
Aerospace is the only industry I know of that has addressed the problem with any success.
They are starting to use a new technology called indoor GPS.
This uses infraRed lasers mounted around the ceiling with the receiver in a hand held measuring tool. The user takes hits on the object to be measured and the 3D coordinate data gathered is uploaded and overlaid on the original CAD model. Boeing developed it.