I don't think you can drop lifesteal, even with Brogni. I think Apoth won't be able to keep up. Actually surprised you even have Apoth in the team - leech + warmaster/gs is all the healing my teams use, and lifesteal heals for almost twice as much as leech does.
I would drop Apoth from the team in favor of someone who hits hard, and drop SS in favor of Brogni. Brogni has the block debuffs on a 3-turn CD instead of 4, so you need less speed to keep the rotation working.
I notice your team doesn't have any DEF down debuffers. That's a major loss in damage. I would recommend replacing Apoth with someone who can do DEF down. Especially good would be someone with counter-attack - perfect would be Martyr if you have her.
Your team would become:
Brogni with high HP - Run A2 last before CB does his turn-2 attack, and then A3 on CB's turn-3
Brakus - sheer damage
Brago - DEF up and ATK down on boss
Occult Brawler - poisons
For the fifth, ideally as mentioned, someone with DEF down, counter-attack, or ally-attack. Martyr fits the bill perfectly, although I'm sure there are other champs that work too.
**EDIT I realise I didn't answer your actual question. With respect to putting Anax on that team - Anax does have the DEF down, so that helps. He could take that fifth spot, although I think you'd do better with a counter-attack / ally-attack champ.
In terms of gearing for your team, you'll probably want your ATK champs to have some mix between ATK and survivability. I'm not great at this one though, since my teams generally are DEF based and not ATK based.
