I like your key bindings even better! However, I still prefer the "beginning-search" instead of just the "search" function:

    bindkey '^P' history-beginning-search-backward    
    bindkey '^N' history-beginning-search-forward

It works and I don't see a downside to this: ^P and ^N still work as expected.

(Why not the cursor keys? Because then you need to take your fingers off the home row.)