well i never self discharged but i know people that did, even after having their waters broken and went on to have normal home births! ditto with the pessary!
my babies were all big and yes they tried to frighten me with that, but ds4 my biggest at 10lb 13oz was my water birth! with no 5, they insisted she was big and i knew she wasnt, a scan said over 9lb and the consultant told me that i wouldnt be able to deliver a 9lb+ baby, i did point out if he read my notes he woudl see i had delivered 4 babies of 9lb+ one of which was almost 11lb, all naturally! he said that was just luck...
anyway dd was only 8lb! the smallest of my 5 and despite her being back to back i was only in labour 3 hrs, yes i needed the drip as i said but i still had a natural active labour, sat on birth ball etc, nad lots of gas and air. i kept mobile and upright and they monitered intermitentally, had their been any issue i would have let them moniter more but she was still very active and i and midwife were happy she was fine so we didnt do continuous monitering depite the registrar getting very cross with us about it!
they have to tell you the facts but yes they can be intimidating, stick to your guns! there is lots on mnet about going overdue and yes it is technically slightly more risky but only a tiny amount, the best indicator is you and how you feel, movements etc, the scan can be reassuring ie checking fluid levels and blood flow through the placenta.
and yes being induced is scary, i never wanted to but mine went really over due, ds3 by hospital dates was 3wks late (18 days by my dates) but my birhts were fine despite being induced, mobile, upright, normal deliveries, no complications at all, no forceps etc or anything.
given how overdue you are and that you have had normal deliveries i would expect it to be straightforward tbh, but yes get checked, re book for home birth and wait a few days and see how you feel, fingers crossed baby puts in an appearance before your next appointment!
most hospitals now dont induce till term plus 14 anyway so going a few days over that isnt that unusual, they did write in big letters on my notes PATIENT HAS BEEN INFORMED OF THE RISK OF STILLBIRTH!!! nice 
but the midwives i met were fine with me going further than 2 wks overdue and none of my babies looked overdue, still vernixy and my placentas always looks great, i always had a good look after they were delivered!
i take it you are doing all the usual, sitting on birth ball, just general stuff to encourage baby to be in a good postion to get labour going? i would do your best to relax, anything stressing you out wont help you go into labour, so hopefully once you get this appointment out of the way and then get home you can chill out and baby will put in an appearance! :) good luck :)