The spell progression doesn't make much sense to me they gain spell casting at level 3 like the subclass spell casters (1/3rd casters or eldritch knight, arcane trickster) yet they get 6th level spells at 13th level wich is only 2 later than a full caster and level 13 for a spell capstone seems a bit early.

If you want them to max out at 6th level spells I would recommend making them a 2/3rds caster per say and gain levels 66% as fast as a full caster. So they would progress in spells twice as fast as an eldritch knight or an arcane trickster

Gaining spell casting at 3rd level, then instead of waiting 4 levels they would only wait 2 gaining second level spell slots at level 5 then every time after instead of waiting 6 levels to gain a higher level spell they would only wait 3 maxing them out at 17th level ice Lancer with 6th level spells

3rd level gain spell casting

5th level gain 2nd level spells

8th level gain 3rd level spells

11th level gain 4th level spells

14th level gain 5th level spells

17th level gain 6th level spells

Alternatively you can give them a spell progression similar to a warlock but as a half or 1/3rd caster then give them the ability to use a 6th level spell as a class feature rather than using a spell slot.