Aliona, I hear you loud and clear on the thick, hot hair issue. This is a big problem for me also and one reason I've never really been happy wearing long hair.
You look wonderful with your longer hair and extensions, and with your new sharp bob. And I think you'd also look amazing with the new cut you have shown. I love the way the sides are done on that one. My only caution would be -- do you know for certain that your hair doesn't wave when layered, esp. in the humidity? Mine is relatively fine but extremely thick; when blunt cut it seems almost stick straight, especially where the air is dry. However, on a humid day, when layered it will wave as much as the Queen Mum, or so it seems. Especially if the stylist goes for a razor cut in a medium length like this. Longer and it has more weight, shorter and the waves don't come out.
If you're certain about the way your hair will fall, I think that would be just gorgeous on you.
However, I also want to argue with you about the pixie. Because, yes, I also have a long face. I don't know what to call my jaw exactly -- it's not sharp, that's for sure. Anyway, although they always say long faces shouldn't wear pixies, I've actually found the reverse. I don't know what it is about the proportions of the face that make a difference. The big advantage you would have over me is your eyebrows.
Having said all that, you could certainly go for this cut now and then try a pixie another time if you wished. Or if your stylist would agree. Those bossy stylists!!! We are going to have to take them in line!!
Also, really glad you have gained the needed weight; that must feel better.