Hi Ted,
I'm a bit of a vocal addict, so I have some expertise on your questions. First - all of the TC products are amazing. The ones built into the Korgs are terrific, and rival the stand-alone counterparts, like the Voice Live2 and such ... there are tons of editable parameters, and loads of presets to get you started.

I'm confused by your gear reference - do you OWN the PA1X Pro and the PA3x? If not ... buying a keyboard just to get a vocal processor is a bit of overkill. If you already own them - then, great! The PA3x is the most advanced harmonizer in any keyboard to date and I've had most of them. (calm down, Fran ... don't even start in with the Roland stuff - the G70 is wonderful in many ways, but the TC harmonizer is a better product)

The biggest trick to sounding great with a harmonizer is to sound great WITHOUT one ... and to THINK, and sing like the counterparts you are emulating. The Lettermen were very bland, average sounding singers individually, but as a unit - they were fantastic. You need to breathe as one, articulate less often and only sing where the harmonies really ought to be. Simply turning it on and singing lead will get boring and robotic very quickly. To start, I'd recommend a basic third above your pitch - that's an easy harmony to make believable ... even on substandard gear. The more voices you add, the better they BETTER sound! lol

Tell me your "go to" gear setup, and I'll get more specific with my advice.
Here's an early example I recorded with a Digitech VR about 10 years ago. It's more of a "Four Aces" sound ... lots of singers n the room! Enjoy.