D&D 5E Variant Multiclassing (AD&D/Gygax Style), help with play balance

[Horwath]

I think I'm going to work on something like that next as it is a lot simpler. But you are giving extra hp? I'd like to have them stay at one hit die per level so I'll probably just have certain levels accelerate your class features by +1 in both classes (maybe 5, 9, 13, 17) so you still end up with 20 dice at level 20 but end up with 14/14 features.

no extra HPs.

your HPs are average on levels where you get both features.
I.E. fighter wizard gets 5HPs(d8) on those levels.