I have a few ideas:
The ice dungeon should be a giant mountain/spire with loot near the top. There should be a path inside/around the spire leading to the loot room. This would have some easy parkour, but the dungeon would be dangerous because of the ice spirits.
The ice spirits should spawn all around the dungeon, instead of spawning around a spawner. The mechanics would be similar to the spawning of guardians in the ocean monument. This means that the spirits are not easily contained and they would be greater in number (which is important since they have low hp)
Lastly, I have a revision of the ice spirits:
-6 health (3 hearts)
-5 damage (2.5 hearts, slow-moving projectile attack, it also inflicts slowness for 5 seconds)
-Can fly like a bat
-Drifts around carelessly until it spots the player
-After seeing the player, it tries to keep a constant distance of around 10 blocks
-Flies around very quickly, stopping at random intervals to charge up and shoot at the player
-When it's health reaches 0 instead of dying immediately, it gains 1/2 a heart and becomes "enraged"
-Enraged Ice spirit will charge at the player and explode with the strength of a ghast fireball, inflicting slowness II for 10 seconds
-When an enraged ice spirit dies, every nearby ice spirit has a 1 in 10 chance of having their health set to 1/2 a heart and becoming enraged
-(This means that killing an ice spirit can set off a chain reaction if there are enough nearby ice spirits)
I imagine the ice spirit similar to a blaze; it is made up of a head and six "rods" rotating around it. However, unlike the blaze, the rods rotate vertically and in unison, making the ice spirit resemble an oversized snowflake. When the ice spirit enrages the "rods" fold behind it pointing backwards, making the ice spirit streamlined like a rocket.
0-2 ice blocks
0-1 packed ice
(the diamond rare drop you suggested seems a bit OP so I would leave it out.)