If you are familiar with Korg already, I'd stick with them, unless you hear something that really blows your door off somewhere else (but be prepared for a whaile struggling with different ways of doing what you are familiar with on the Korg).

PA800, or PA2Xpro (if you want to play full piano parts) would seem a great suggestion.

Yes, the Audya has definite stability OS issues at the moment, and is, unfortunately, just a bit too 'bleeding edge' to recommend right now. Wait a few weeks while OS3's troubles are documented, and you'll have a better idea of where that one is (and it's way outside your price point, anyway).

Alternatives to look at might be a used T2 (T3 is a bit more than your limit). Yamaha do have a fairly large selection of praise and worship styles, if that's what you are looking for. But you'll need a speaker system for it.

An S910 will save the church at least a grand, and still do the job nicely.

Not sure, for a big church gig why speakers are a big deal..? They aren't going to be loud enough for the church anyway, in all likelihood. Having to have them severely restricts your choices (Audya, T2/3, PA2X, for instance).

At this point, if 61, and speakers are mandatory, PA800 then PSR S910 seem your best options... in that $2000-3000 range, anyway. Me, I'd go with what you are familiar with, and get a PA800...