The test of a proper fitting ice climbing boot is to find something in the store, a staircase for instance, and kick the crap out of it. If you don't feel it in your toes, that's at least one positive checkmark. The invernos are like a cast on your foot, and generally have poor ankle flexibility, and weigh a ton. I've snowshoed approaches to ice climbs with them, and it feels like the proverbial concrete shoes. Not recommended.
But since you own them already, and they are clearly not fitting very well, I'd still try to find a higher volume inner boot.