I would just be using 3 contactors and a timer, one for the main supply, 1 for delta and 1 for the star contact, the star contact just shorts the windings so does not need to be FLC rated, the only need for a Picaxe is for the timing and possibly operating the contactors, but a timer is really all that is needed as you use the contacts of the timer, one thing that is essential is that the Delta contactor and Star contactor are interlocked so that they cannot both be on at the same time, there are mechanical interlocks available with contactors and you must also electrically interlock them too.
I don't know what 18hp is and I'm not going to google it either, but for anybody to do this sort of wiring, you really need to have a license to do this type of work, fortunately I do....