For some reason all the books have this bullet Speer 130 gr BTSP in the 7mm-08 seated back at 2.73" COAL, . When I actually measure this bullet in my rifle it touches the rifling at 2.81". How close to the rifling can I seat a bullet before I start to see increase in pressure?

I would think that you could seat at 2.80" or less and not have a pressure problem. Velocity will also decrease the farther from the lands you seat.

But you should be able to find an acceptable load at 2.78" which would be .030" off and not lose too much velocity and still be completely safe (other factors being under control)

The bullet ogive is much more relevant than the actual OAL regarding chamber pressure.
A car can easily drive over a curb with a little running start; but if you park right up against the curb and step on the gas - it requires a whole lot more force to start moving.
If you are seeking the ultimate accuracy (and if you don't plan to use your magazine) you should start at least .001" behind the rifling, and try reducing the OAL in .003" increments, until you come up with the most accurate load. I like to start at about .005 and work back to about .050 ..I usually find my OAL somewhere in between.

thanks for the info, I will try 2.77 and there about see what happens. Just don't want to get into unexpected pressure spike.