"Stretch your cervix" = "stripping of membranes" = forcibly reaming out your most private parts = risking infection = attempting to jump start labor instead of letting your cervix slowly and gently open like the beautiful flower that it is!
I'm really glad you cancelled your appointment! You might want to consider, instead of planning to go in if you're two weeks overdue, just leaving the option open of not going back there until and unless you (a) start labor, or (b) sense that there's something wrong. Because you might start labor tomorrow (wow!), and you probably won't go two weeks past date (although most first babies go four days past, if I remember correctly). And if you're paying attention to your body's and your baby's signals, which you appear to be doing, then you're likely to know if something goes awry ... and THEN you can ask the interventionists' opinions.
But if you don't want them intervening when it isn't necessary, don't go giving them the opportunity.
Did you know you can check your own dilation? If you reach inside and touch your cervix (be sure to have extra-clean hands while doing this!), a non-pregnant cervix will feel kinda like the tip of your nose. Near the end of your pregnancy, it will feel more like a soft pair of lips puckered up for a sweet kiss! If you can easily insert one fingertip inside, it's 1 cm dilated; two fingertips = 2cm, approximately. Midwives know, with practice, how to measure wider (it's a matter of experiencing repeatedly the appropriate positions of their fingers, not about inserting ever more fingers inside there! They're measuring diameter, not volume.) Also, be aware that the way different caregivers measure is sometimes widely varied: a less-experienced person might think you're dilated to eight when a more experienced person might judge the cervix to be open much less.
One more tip: when you reach eight centimeters (called "transition" -- the last two cm are that time just before it's time to push the baby out), the best "symptom" is a marked change in how you feel emotionally -- when a woman reaches transition is when she's most likely to say "I can't do this anymore! I can't take it! I want to go home!" or whatever ... and that's the time when it's most important for a husband/partner/doula/caregiver to say, "You CAN do it! You ARE birthing this baby! You're in transition, and you're very close to being able to push this baby out! Hang in there, sweetie!" The panic is an important signpost, more important than what (particularly inexperienced) fingertips can judge of dilation. In fact, sometimes women report that they've recently had their dilation checked and reported significantly less than 8 cm, and then they get to this stage, and their (nurses or doctors, usually) caregivers tell them it can't possibly be time yet ... and then they're pushing, so their bodies' and their psyches' clues were on-target regardless of what the "professionals" say.
Labor is not a straight-line progression: some women jump from 3 cm to 10 in a matter of an hour, many progress relatively constantly about 1 cm an hour, while others hang out at 7 cm for a day or more before proceeding to transition and pushing the baby out in a big hurry (that'd be me!).
All this said, and alongside my strong pro-homebirth midwife/anti-OB position, I do feel a tiny twinge of worry about offering all this advice when I'm not your caregiver and I'm not even a professional (just someone who's read ALOT and had my own experiences). It's not that I worry there's anything wrong specifically with your baby or with you, but in general. Birth is safe, yeah, and in probably 98% of the cases, should be left to its own natural progression. But birth is also a part of life, which is unpredictable and includes the experience of "bad things," the exceptions that prove the rule. When we become pregnant, we place ourselves at risk of the most heartbreaking experiences. So trust your body, trust the signs it and your baby give you, and if YOU feel there's something wrong, get yourself to a doctor or hospital right away, and don't imagine that some advice you read in the Internet is more important.
Because, in the end, nobody's more important than you and your baby.
Keep the faith!