The Crimson Binome
Hero
For the sake of simplicity, I think it would make more sense to retain your base class hit dice for all levels. This isn't true multi-classing, after all. You're mainly a fighter with some lower-level wizard abilities, so you should still be a fighter in every way that counts.That's funny how the eldritch knight had, indeed, the same level progression as a lvl 7 wizard. Never noticed that.
When you would gain another class level instead of your archetype feature, would you use your class HD value for HP or the multiclass class' HD?
From a balance perspective, it seems like it would strongly promote certain combinations rather than others; and access to low-level wizard spells is certainly not sufficient to justify a fighter being less capable of taking a hit. They aren't going to spend a third of their combat actions to cast spells from the back line, or anything.