I added this line to the ~/.zshrc above the source $ZSH/oh-my-zsh.sh line:
export ZSH_COMPDUMP=$ZSH/cache/.zcompdump-$HOST
Then, when we source $ZSH/oh-my-zsh.sh, the compinit command dumps to that new location.
Here’s where compinit is in oh-my-zsh.sh.