I don't think the 1NZ-FXE ECU would work without the HSD. I wonder if a FE ECU would work? I think the 1NZ-FE actually uses Atkinson cycle at idle and low load, I was looking at the VVT-i timing chart for the Yaris and at idle/low load the intake stays open until 52* ABDC. That's 29% of the compression stroke.
http://www.microimageonline.com/down...als/Engine.pdf
http://www.mr2.com/files/mr2/techinf...ata/1nzfxe.pdf