How do I add additional info to promote and deploy emails in admin?

You'll need to extend the PromotionSystemEventConsumer class and override the buildEmailVars(...) method.

protected Map<String, Object> buildEmailVars(SystemEvent systemEvent, boolean critical, String message, SandBox sandBox, Date deployDate) {
    Map<String, Object> vars = super.buildEmailVars(systemEvent, critical, message, sandBox, deployDate);
    vars.put("myVariable", myVariable);
    return vars;

With this method additional variables can be added into the vars map which will then be available to the email template.