Check the fuel pump if it has one. My LGT165 bogged in high grass when the pump was dying.
You can't check compression on a K series Kohler at cranking speed due to the compression release. The Kohler engine manual says to turn the engine backwards against compression and it should bounce back. To check compression with a gauge, the engine needs to be belt to another engine to crank it above 1000 rpm to get past the compression release cut out point.