Probably not without your valves destroying the pistons on the first few revolutions. Domed pistons with valve recesses probably the only way for this radical an increase in compression. How are your metallurgy, casting, and machining skills?

For a primer on self experimentation with piston design and manufacture, rent "The world's Fastest Indian (motorcycle)" - true story about how an old geezer in Australia (played by Anthony Hopkins) breaks the world's motorcycle speed record at over 200 miles per hour at Bonneville 30 or so years ago. The shelf with blown pistons and other sundry parts says it all! "Next time", he says after the latest disaster, "I'll try three parts Chevy, two parts Ford." (for the new piston castings). Great story!

Of course you would also need a CVT to take advantage of the enormously expensive Atkinson mods, on the extremely unlikely and costly chance that it would do anything but self destruct unless done by anyone less than Toyota's R & D stable!

And of course the HiHy's engine is not an Atkinson design, so you would be breaking new ground as well as the bank. There may be a good reason beyond the R&D expense for a projected limited volumn model that Toyota left it as a basicaly conventional higher compression design.

Good luck, great dreams!

Pete