How to deal with fixed registers?

I've been loosely following along this series and I'm starting to feel like doing register allocation top-down (explicitly directing where to put values into instead of loading values into any register) to deal with fixed registers might not play well with how typing is done. By fixed registers, I mean instructions where some operands must be in specific registers. For example, The Z80 can only use `A` or `HL` as LHS for math operations.