Some things to note.
1. Elysians don't have the Command squad restriction that the codex guard do. (But they don't get Warlord traits, Relics, or Doctrines either) So you can run more of those.
2. Even if you want to be "Nice" and play with that restriction I would recommend swapping 1 spearhead for a Vanguard and droping the Infantry squads for Special Weapons teams.
3. If you not completely dedicated to running pure Elysians then consider making one spearhead a Codex:
AM Detachment so you can pick up the Strategems, Warlord Trait, and Relic.
4. Try to fit in an Officer of the Fleet. He will let all your dudes reroll ones on a specific target and has a decent other little ability too.
This was my take on a similar list to yours.
https://www.dakkadakka.com/dakkaforum/posts/list/741456.page