While this is Alpha Legion, I do not proscribe to the view that they need cultists,cultists,cultists. I dislike cultists on an aesthetic level and feel strongly about it!
Have you given any thought to using Astra Militarum or Tempestus Scions then? The chaos codex may only give you access to cultists, but the Alpha Legion are known for using highly trained operatives and guard veterans and storm troopers definitely fit the bill in that regard.
Chaos Lord with blade of the Hydra
Beyond second HQ filler in a battalion, I honestly don't see much point in the exalted champion. Your honestly better off running a second lord with a power axe or fist.
Terminators x5, 1 Power sword, 4 Power Fists, all combi bolters
The second lord would be especially good here, helping to augment the fists while your primary lord buffs others.
Chosen x9, 3 power swords, 2 power fists, 1 flamer, 3 chainswords
Like this squad, your primary lord probably belongs here.
Dreadnought with multi-melta and powerfist
Honestly I feel the same way, overall good choice.
3x Chaos Space Marines x10, Aspiring Champion armed with a fist, 1 plasma gun and 1 missile launcher
Overall good choice though I'd stil consider swapping one out to heavy bolter/autocannon and flamer with a sword or maul armed champion.
I proscribe to the idea that 30 CSM is a lot of bodies to deal with
In ten strong squads in general yes, but you'd also be quite surprised with some armies now. (having to take 10-20 saves at normal armour or at -1 will whittle squads down fairly quickly.)
Predator armed with autocannon, havoc launchers, lascannons on the sides and a combi bolter
I'm a fan of the auto-las so go-go baby!
Its a good tank/monster buster
Havoc squad with 2 lascannons and 2 missile launchers
Personally I've never been a fan of havoc/devestator squads with no ablative wounds. I'd suggest dropping a missile launcher for some more bodies.