Even in 3.5e, warlocks had invocation with effective spell levels all the way up to 9th level (such as dark foresight). In 5e, they also get 9th level spells.
Besides, you're already giving them most of the 9th level arcane spells (dominate monster, mass hold monster, Mordenkainen's disjunction, power word kill, summon monster IX, wail of the banshee, etc). You're just arbitrarily making them 6th level spells for this class, which only serves to reduce their save DC. As people have already pointed out, the low save DCs are going to be a problem. Wouldn't the easiest solution be to just give them a spell progression that goes all the way to 9th level? They'd still be getting the exact same spells, they'd just be at their true level.
I'm not trying to be argumentative, or anything, it's just some food for thought.