I find that, as my thighs are one of the major parts my body prefers to keep fat, I have some of these issues.
The CKR is my preferred way to invert, currently, and there's a bit of a trick to it- place your ankle on your knee. Like, your knees shouldn't be close to each other! This way, they aren't getting in your way (and, depending on the thickness and length of your legs, could be helping out) and you can properly lean back, allowing most of your weight to rest on your lower leg (of your bent leg, obviously).
For the CAR... well, I managed to do it twice the other day while skyping with Krissikiki! This is quite a record for me! This was the ONLY move that I've ever fallen off the pole trying to do. It still scares me a lot, but I'm starting to understand it. You don't want to squeeze your legs super tight as you're leaning back... Cross your ankles and slowly allow your bum to drop, rounding out your back so that your feet start pointing toward the ceiling. Once you feel you've dropped as far back as you can while still holding on to the pole, then SQUEEZE! Turn your knees in toward the pole, clench your butt, and really try to get everything involved! Then, test it!
Take things slowly- seriously! I like doing things from the ground, first, and for these moves, doing a sit UP from the floor, rather than laying back into them. If you can sit up in these moves without the use of your hands for grip, then go from a low pole sit and see if you can duplicate it.
Us lades with lovely legs really CAN do these moves, you just have to adjust for your own body type. Not everyone is going to do everything exactly the same!
And, as a disclaimer, these are my own methods! You might find that the total opposite works better, or that something I haven't thought of comes into play for you. But... play with it. Adjust the height, start from the floor, see how far apart or close together things need to be to make it all work.
And yes... sometimes they hurt really bad ;)