Honda GCV135 stalls on low RPM?

Hi, I've just brought my Honda Izy lawnmower (GCV135 engine) out of storage (2 years garaged). It started first time but will run only at full throttle (3000 RPM). If we lower the speed to lower than half throttle, the engine stalls.

Here's what we've done so far:

1. Carb cleaned and new gaskets added
2. Fuel tank cleaned and new fuel added

Does anyone know what the issue might be? We're fairly competent DIY'ers but don't want to mess around too much and break it as it does actually cut the grass.

The only thing that can cause an engine to run at full rpm, and fail at lesser rpm is a fuel or carb problem. When you cleaned the carb, did you remove the welsh plugs, and use an ultrasonic cleaner? I have had to sonically clean a carb three times before it got all the varnish out. If the mower sat for 2 years with fuel in the carb, you might want to re-clean the carb, or replace it.