Transition 1 inch tile to 1/2 inch laminate

Hello everyone. I am doing my first floor installation. Installing laminate floor in bedroom that is connected to a bathroom. Bathroom has tile and transition that is 1 inch high. New laminate is 1/2 inch high. Would like to get input on the best way to transition in this situation. Trying to be practical and not remove the tile transition.
I included some pictures showing the floor and my ideas so far (laminate flush mount reducer). Appreciate any ideas or input

 

You have the right idea. Depending on the expansion gap requirement where the laminate 'meets' the tile transition bring the laminate as close as possible to the tile so there will be good support for your transition/reducer as it will be 1/2" thick max at its thickest edge. If the tile transition has beveled edges (usually 45 degrees) consider putting a reversed 45 degree bevel on the edge of the transition/reducer so it will be tight to the tile transition.
The nails securing the transition/reducer should penetrate the subfloor.....you can use a separate wood filler strip in this area. The filler strip can be a piece of your laminate.