I bookmarked
This Page as a quick reference to what each Z-Status Move does.
The Strongest Support Effects are the following:
Normalium-Z:
Tier 0: Heals 35 HP (+Effect)
Stockpile (Boosts Defenses)
Heal Bell (Heals whole team of Status)
Refresh (Heals User of Status)
Psych Up (Copies Opponents Stat Boosts/Drops)
Conversion 2 (Changes Type favorably)
Transform (Mirrors opposing Pokemon)
Tier 1: Permanent Sharp / Great Atk/Spe Boosters
Belly Drum (Costs 20% Max HP and Maxes Attack, best used at 70% Max HP.)
Bestow (+2 Speed)
Me First (+2 Speed)
Recycle (+2 Speed)
Splash (+3 Attack)
Tier 2: Permanently Boosts All Stats
Celebrate
Conversion
Happy Hour
Hold Hands
Sketch
Tier 3: All Other Effects
[Switch=KO] Darkinium-Z:
Tier 0: Parting Shot (Heals 30 HP, Resets Secondary Status)
Tier 1: Taunt (It's a Taunt you can use during Taunt, it also raises Attack)
Tier 2: All Other Effects.
[Switch=OK] Darkinium-Z:
Tier 0: Parting Shot (Heals 30 HP of replacement.)
Tier 1: Memento (KOs Self and shreds opponents stats, Heals 30 HP of replacement)
Tier 2: Taunt (It's a Taunt you can use during Taunt, it also raises Attack)
Tier 3: All Other Effects
Ghostium-Z:
Tier 0:
Spite (Heals 35 HP, Lowers Opp EN)
[Doubles+ Only] Destiny Bond (Becomes Center of Attention while using Destiny Bond)
Tier 1: Curse (Costs only 20 HP when used at 30 HP below max)
Tier 2: Boosts All Stats
Trick-or-Treat
Tier 3: All other Effects.
Grassium-Z:
Tier 0: Aromatherapy (Heals 35 HP, Heals Status of whole team)
Tier 1: Forest's Curse (Raises All Stats)
Tier 2: All Other Effects.
Icium-Z:
Tier 0: Haze (Heals 35 HP, clears all stat boosts/drops both sides)
Tier 1: Mist (Heals 35 HP, prevents mons stat drops)
Tier 2: Aurora Veil / Hail (Permanently Raise Speed + regular effect.)
Psycihum-Z:
Tier 0: Heals 35 HP (+Effect)
Teleport (Evasive + Healing, or Switch Out/Secondary Status Reset + Healing)
Tier 1: Permanent Offensive Boosts
Ally Switch (+2 Spe)
Heal Block (+2 SpA)
Psycho Shift (+2 SpA)
Tier 2: All Other Effects
For pretty much every other Z-Crystal, you're looking at boosting your damaging coverage or a few of the +1 Spe Effects from Weathers or Terrains.
For obvious reasons Normalium-Z is the elephant in the room, as its Healing effects fat outweigh the value even of Giga Impact / Hyper Beam based Breakneck Blitz (+35HP vs 20 BAP Non-Effectiveness Boosted Damage). It might be a reasonable policy that only actual Normal-types could use its Z-Status Moves twice. Psych Up's distribution is so ubiquitous that it's easier to make a list of Pokemon that DON'T get it than a list of Pokemon that DO.
For all the other "strong" Z-Crystals,
Spite has some interesting users (Rhyperior and Aggron lines for example) as well as mostly Dark types with no other form of recovery. It might be wise to apply the same restriction on Ghostium-Z to Normalium-Z. Haze and Mist have out-type distribution primarily to Poison and Water types, respectively. The longest list of Teleporters actually comes from Gen 1 and most of them have other means of healing. That said Evasive Z-Teleport seems pretty nuts. Everything with Aromatherapy [Except lol Xerneas] gets an HP restoring move (usually Wish or Synthesis), but it's still there and it's not reliant on Sun to maximize healing.