I can successfully add a calendar, but unfortunately I can't embed that calendar on remote pages like I want to, because it's not set to public!
I can't find any references to setting the calendar's sharing settings/permissions to public.
EDIT: Found some more info: https://developers.google.com/google-apps/calendar/v3/reference/acl/insert
Seems like this is what I need, I'll report back with exactly how to do this..
EDIT #2: I'm getting good at this!
$rule = new AclRule();
$scope = new AclRuleScope();
$scope->setType("default");
$scope->setValue("");
$rule->setScope($scope);
$rule->setRole("reader");
$createdRule = $service->acl->insert($createdCalendar->id, $rule);