I would remove the tile. Then put down the sub floor as you described (not sure about your choice of material) over the left hand section. If what you then have is fairly flat, cover the entire floor with 1/8" luan plywood (I think this is what they used in my laundry). The final covering was vinyl plank.
I would remove the transition strip and place the new flooring down and put the transition piece back on. If you glue something on top of the transition piece, it will be a trip hazard and will, in a short time, come loose.