My suggestion and my favorite jeans are vintage straight leg Levis. I find them at thrift shops and vintage shops. Even if you have to pay to have them altered, you'll have a great pair of jeans for a fraction of the cost of the fancy brands. I own a few pair of expensive jeans and they look cheap next to my vintage Levis. BTW, I suspect the girl in your third link (LA Cool & Chic) is wearing vintage Levis.
Yes! Men's jeans are an alternative. That's where I find most of mine.:D
Personally, I only like spandex in jeans if they're skinnies. Otherwise, I think classic denim just looks nicer and ages beautifully. Since you mentioned that you like the spanx effect, why not just wear a spanx? I do, under just about everything. Personally, I think they make everyone (no matter what size) look better by smoothing out the lumps.
This video may be helpful.
BEST STRAIGHT LEG JEANS CHALLENGE: MADEWELL, H&M, TOPSHOP + MORE!!!
https://www.youtube.com/watch?v=kJ5v2hz8kG4
Good luck with your search!