Have you tried using KPlayer like soft synths "normally" are used: using synth rack?
Also, did you read my post above? Is there a standalone mode for KPlayer?
I'm not at all sure if LE has it, but in other versions there's a setting called something like "Zero controllers on stop". I wonder if it's possible that it has something to do with this.
And an important thing: Have you checked which settings, if any, change when you press Stop?
Is the MIDI channel , track ins and outs, everything, what it should be? The levels?