Man you are awesome; I have been looking for definitive info on the i43 weapons for days now. I spammed like 30 battle leves at Bluefog last night with no luck on any i43 weapons, but I purposely avoided "Don't Forget to Cry" because it seemed to take the longest of all the leves and I assumed that the chest spawn would be similarly random for all leves (yet to be proven or disproven definitively). In those 30 leves, I had maybe 13 red chests (crap item) and 6 blue chests (aetherial); the 6 blue chests yielded:

2x: http://xivdb.com/?item/1787/Aetherial-Mythril-Bhuj
2x: http://xivdb.com/?item/1717/Aetheria...oiseshell-Hora
1x: http://xivdb.com/?item/4040/Aetheria...n-Hunting-Belt
1x: Something else I've forgotten

Will try your leve suggestion and see how it goes.