I don't have the sets I used anymore, and don't care to make them again either. However, Upbeat has recently-ish started doing what you wish to do, you can use him for reference for Gear and or otherwise.
I know the strategy for most of any of the mobs though, more or less.
For Charybdis specifically, it's just a Bind/Gravity and Nuke/Dot battle whilst you run around those rock things in it's camp. Sub NIN of course.
I wouldn't doubt it possible to straight tank it, though I personally never did try. If you try that route, pick up a ceremonial dagger so you can hit 0's to avoid TP feed, whilst your En spell damages it.
It'll strip shadows like mad, but I don't think it's melee attacks hurt alot with Phalanx, Protect IV, and a Tav Taco (this will be post defense adjustment too, so defense will be more effective than it was back in the day.) Make hybrid melee set with some PDT, as it can and will occasionally attack more than 3 times.
Full PDT with shadows down, put shadows back up and reapply Stoneskin. Keep debuffs on it obviously, Paralyze is particularly potent against it if memory serves.
Oh, also, there may be a Devil Manta in the room with Charybdis, if you go the kite route and want the full challenge experience, you would be expected to deal with it. People use to readily ensure one spawns in that room so any RDM soloists would have to deal with it. Pretty simple though, you Gravity it and make it deaggro continuously, it doesn't really pose much of a threat.