I absolutely would not ask for a c.section now. there is no medical reason that you need one, and it is major surgery, not just something to opt for when you are tired of being pregnant, but i absolutely sympathise with how you are feeling.
your body is going to get going , if you have had a show and are having ctx, then things are getting underway.
if i was in your shoes, i would be taking this time to rest as much as possible, with no other children to look after, lolling around in the bath and conserving my energy.
sex & nipple stim can help to get things going and to make the ctx a bit stronger. next time you see your midwife, you could ask her for a stretch and sweep to see if that tips you over the edge into labour
it would be very unlikely that you would be induced or given a c.section with no medical indications
also., an induction of labour ,if your body is not ready can take days and be a lot more painful than a spontaneous labour
if you are in pain, take paracetomal and try having lots of baths, or use a TENS machine
am sure you will be holding your new baby soon enough