21 charges of Mesmer Skin
Cast Cost: 12.5 energy

Energy Siphon Aura:
0.6 energy per second

12.5 energy / 0.6 eps = 20.8333s

21 seconds Invulnerability
20.8333s to recast

Add Crimson Archon Shards to be more invincible.

Notes:
Zenurik 'Inner Might' is a 60s free cast with some exceptions.
Watch out for 'Nullifiers'.
Add Forma to increase Umbral mods if you want.

Mesmer Skin rounds up with 0 adding 1 second of invulnerability with extra effects, Energy Cost rounding is exact.