There are more than only the classic modulation effects in the KPA.
Try the "pitch effects" and the "ring modulator" to get fine modulation effects.
Yes - ring modulator - it must not sound strange like a ring modulator in case you use very sensitive settings:
I use this settings:
Ring modulator - Manual 5.1 - Mix 60%
Here is the result:
(first clean then with ring modulation effect)