Bob offers good advice on tire selection. This is an area I'd like to see more practical research on. I've been meaning to do some, and I suspect Pete Riegel and others must have visited the topic. I don't have the answers today - but I have some clues...
I think there may be a trade-off that you, the rider, need to balance based on your knowledge of the features of the course to be measured and the weather expected during the rides. You may want to have a selection of tires available for different situations.
One of the biggest challenges to good calibrated bike measurement is change in ambient temperature during the rides or between calibration and rides. A result of temperature change is a calibration finish-constant that varies from our working-constant(s). Big temperature changes may yield big variances in your tire diameter, and therefore differences in calculated measured distance over the course.
Our procedures suggest strongly how to handle it. We will usually err on the side that produces the longer course. In Canada they take the average constant. In the USA we take the larger constant, but are given discretion to take the average - if we can justify it. But, I think I'd rather not have to "err" at all!
Here's a pertinent observation from a point-to-point marathon team measure this summer: I had cross-bike tires. These tires are larger than racing bike tires and have some tread (i.e., more air volume, more rubber). The other riders essentially had the same diameter rims, but used the skinny little racing style tires. We pumped up to spec, calibrated, rode the course, then re-calibrated as usual.
I felt I got a slightly better ride than the other two riders. I got better traction, rode up all hills in a straight line, never had to walk, held the SPR well over both solid and loose terrain. That part is good. Note, there was a significant temperature change during the ride.
But upon calculating the finish constant It looked to me that I suffered the biggest variance in tire diameter due to the ambient temperate change! That is less good.
We theorized that the physically lower-profile tire may experience less volumetric (air) expansion and that would be a real advantage toward attaining an accurate measure, as opposed to just a measure that is not short.
So, which tire type would generally be the best?
I wish I knew.