If you're using the Gain knob to add distortion you'll probably be happier with a cleanish profile plus any of the distortion pedals. The "Muffin" is fantastic, and the "Fuzz DS", while not perfect, responds like a fuzz box to changes to the guitar's output volume and pick attack. It's a very good fuzz effect. The "Green Scream" as mentioned is excellent with clean profiles and single coils but you might want to set the tone a tad dark.
The Gain control can be on the harsh side past about halfway but it's a quick method to get into rock-out mode. It's actually very useful for beefing up a bass or keyboard but some of that effect is likely just volume. It also works well in reverse to nicely clean up some distorted profiles, maybe even better than going the other way.
There are some great high-gain profiles that are either already on your machine or are free at the Rig Exchange. For amazing OD tones I'd start with browsing through your available rigs. I like to find one that's close to what I'm looking for and start playing with it.
I find it surprising that you've not found any good OD tones in a device that excels at them. The KPA's EQ effects are very good at dialing in tones and you may find adding one or more (multiple EQs seems to be fairly common) improves things.
A lot people on here like to hear recordings of what's being talked about, so that approach might be useful. SoundCloud seems to be the go-to place for that.
The main thing I find is that a solo guitar only resembles the sound of a guitar in a mix -- live or recorded. What sounds great on its own will usually sound less so in a mix. The tones that I go far generally cut all of the highs and lows and exaggerate the mids. They sound so-so by themselves but are huge in a mix when they need to be.
You probably already know most of this but it took me some time to work this stuff out, so hopefully this is of some help.
