Actually, I have had thoughts along the same lines, except that it would be tunnels - many of them each hundreds of feet in diameter and tens of miles long - instead of just one. Each would leach off a portion of the outflow. The trick would be to create portals that could be both strong enough to resist the building pressure yet still sufficiently thin that they could be breached in a controlled fashion (probably using nuclear shaped charges) when the time came to directly tap the magma underneath the dome and draw it off laterally.
The problem is this would be the largest civil engineering project in history and it would be undertaken to prevent a catastrophe that is going to happen at some unknown time in the future. Tough sell to the taxpayers and corporations.
How do you pay for such an endeavour? What present benefits can be derived from the situation to make the project more appealing?
Pay for it by taping the radiant energy of the supersize magma pool to produce incredible amounts of electrical energy and selling it at a discount all over the world. This would involve sacrificing the visual beauty and natural environment of Yellowstone to erect the hundreds (or perhaps thousands) of geothermal energy plants needed to draw heat from the resource. What surplus energy that is not sold (or is otherwise allocated to the task) would be used to power other massive high energy cost projects like, say, filtering the atmosphere, oceans, and lakes of harmful pollutants, desalinating sea water on a massive scale, extracting dissolved minerals out of the oceans, converting the entire transportation infrastructure to electrical power. (A side benefit might be to leach off enough heat to thicken the cap over the magma chamber and forstall the eruption.)
The enginnering problems can be mastered if humanity has the will to think on the appropriately epic scale of effort.
enginnering = engineering