Wye-Delta Start is not a soft start! If you ever need to replace the motor be sure to get one with 6 leads to work with the reduced current start system. Wye-Delta Starts are widely used in areas with poor power available. Some areas of Japan & Europe and almost all "3rd world areas." Do the controls unload the compressor when full pressure is reached? If no air demand, for a timed period is the motor shut off? Do the controls allow you to adjust that? Running unloaded the motor will consume 60% +- of full load. When "Off" no power is used BUT at start again there is a surge in power needed to start everything turning.
You might want to reduce the cycling of the new compressor by adding more storage. A beam saw has low air demand, don't know what your drill will use. The CNC will use the same amount per unit of time regardless of the # of hours it runs. The two things there that cost a lot of air: the air nozzles that blow on the tooling and the blow gun to clean the table.
Go to Kaeser's web site and look @ their recommended air system for components needed. I forgot one on my earlier post, coalescing filter. Clean, dry air is worth spending some $ to get given the cost of equipment and down time. Once the pneumatics of a tool are fouled with oil, water & dirt it is almost impossible to clean them out.
Let us know how it works out.