For ex:
Susano for 320
Shinryu for 335
Byakko for 355
Tukuyomi for 365
Suzaku for 385

For normal:
O4N for 330 uncapped
S4N for 360 uncapped
A4N for 390 capped 1 item / week

Maybe farm O4N for the 330 weapon and then go for for the 360 weapon? I think those might be easier or faster then EX's considering how many pugs wipe on those even with the 'duty completion' box ticked.

What's the Ilvl of your armor?

I took a break from the game since second raid and currently I have 360 armor and the Byakko ex weapon (total Ilvl is 359) and I have no trouble doing experts with those.