Narshe defense is kicking my butt

Title. Most of the game's been a breeze so far, but Kefka simply steamrolls me at level 16. Should I grind more, or am I just not using enough brain cells?

Strategies I've tried so far:

1. Celes / Edgar / Locke with Celes spamming runic, and the boys attacking and healing when needed. Fails because every once in a while Kefka will focus hard on a single character and kill them.
2. Cyan / Gau with focus on heavy damage. At one try I managed to inflict between 3000 and 4000 before I died, and Kefka showed no signs of slowing down.

I'm thinking of attempting it with a party of four, but then it'll mean either leaving one member out, or doing the entire battle with one 1-person party.

Also, what's the deal with losing not being a game over? Is this a carry over from vanilla, or a T-Edition thing? When I lost with all three parties I thought the game would end, but instead everyone is reduced to 1 hp.

EDIT: 4-man party did the trick. I put Cyan into the fridge, then made one party with Edgar (spamming bio blaster) and Terra (spamming cure) to clear the trash, and another with everyone else specifically to battle Kefka. With Sabin and Locke spamming potions, Celes on Runic duty and Gau doing all the damage, it worked. As a bonus, Edgar and Terra got a lot of levels.

You solved it, and nice work, just putting some other info here to answer the questions you asked and for anyone else seeing this or struggling:

I believe the reduced to 1 HP is a vanilla thing, as the only game over is if Banon is reached. It's the same with the "Protect Terra!" scenario at the start with the Moogles. You could in theory cheese/abuse steal on Kefka with Locke to farm him for Elixirs and Hi-Ethers if you wanted to.

As for Kefka, the strategy all-around here is do a 4 man party and focus on using just them. Put the other characters in the 2 groups and forget about them. If you decide to use Cyan, the trick to keep him up is have Celes use Runic, THEN have him do Bushido and she'll take the Bio, and he's free to continue damaging without retaliation. Bring Celes and have her solely focus on Runic. Sabin or Edgar as a heavy hitter to go with Cyan and have Gau do Mandragora for Sunbath healing, or have him do a damaging rage while you have Sabin/Edgar/Locke focus on healing only. Give people confuse/toad resist also if possible. Should be able to win no issues here with this method.