They simply can't get the weight down - unless they switch to Rotax , something they don't want to do because a lot of schools would be more comfortable retiring their 150s if their replacements were at least running engines their mechanics are familiar with.
They either have to get engine weight down or airframe weight down, preferably both. The only way to reduce airframe weight and retain strength is to go to a different material. Cabon fiber/kevlar is really the only option, without shrinking the size.
Don't get me wrong, I'm not a composite fanboy, I actually prefer metal airplanes. But It's shocking how light and strong carbon airframes are; it's the primary reason the early CT line and lately Pipestrel can flirt with and sometimes exceed 600lb useful loads where most other LSA are hovering around 500-550lb useful.
I'd really love to see what a talented team of engineers could do making a clean sheet design with two design goals:
1) Minimize aircraft weight.
2) Maximize aircraft utility.
Those two conflict somewhat, but all designs are a compromise...