I can only tell you what I'd do :)
I wouldn't have anything invasive like a S&S before my due date. Probably not til I was 7-10 days over actually. I just think your baby will come when he/she is ready and trying to force it might make you have a harder labour. You will go into labour soon. If you go overdue I doubt it will be further than with your DD.
It sucks that you would have to go to another hospital if you're overdue, that's ridiculous to not even give you til 1 wk over before having to change.