This is just my analysis Che:

You could make the Katanas work more if you gear Basch to have a high magick power, since a Katana bases damage on a character's magick power and attack power. You should also get Basch's speed up, by either equipping a cat-ear hood, the Genji gloves, or just casting Haste on him. That way you'll have a greater chance of getting a lot of combos. Also, the thing about being sucky against the undead. Are you sure that you didn't mistake a Katana for a Ninja sword? All Ninja Swords have the Dark element added effect and undead tend to be immune/absorb dark damage.

I like Greatswords for Basch personally, but when I have him equipped with one, I make sure that he's not the one leading my party, since enemies tend to go after your leader more. I make sure that my leader is geared for strong defense.

Have you thought about using a Pole at all? They aren't so good against enemies with high magick defense, but they add +25 evasion and can deal out some pretty heavy damage when you get them to combo a lot. The boost of evasion is good, since this is a two-handed weapon and you can't equip a shield.

I hope I helped a little bit, and good luck!