Get an E series machine all problems solved. I make a cap to go over a live center body. Then the live center body can into a cavity make the cap with a light press fit into your part.
Load the tools by hand to eliminate your toolchange problem. Can be easily done using the right codes to index the mill spindle then a M00 switch to Manual mode and done.
Last problem would be a parameter. Go into the electric book and look for the loop that shows the sensor for the W axis being at the home position the Ladder position is listed there. Now you need to go into the ladder logic and see if it tells you the parameter that controls that place. This way might yield you better results to find the correct parameter than the guessing of the people at Mazak.