Hey, I read your post! I'm exactly the same like you! I'm looking for exactly what you said. anyway, one of the best, and most popular Shape shifting cube, is the Mirror cube.
Here, It's aroun 6 bucks i think. It's really good ,and said to have perfect turning

Here is a link if you would like to check it out
Cubicle:
https://thecubicle.us/advanced_search_result.php?search_in_description=0&keywords=Mirror
Amazon:
http://www.amazon.com/gp/product/B0...rd_t=36701&pf_rd_p=2079475242&pf_rd_i=desktop
Also, I just purchased a new puzzle I haven't tried yet! It is supposed to arrieve tommorow, here. You probably have heard of it, it's the Pyraminx. It's a fun, different cube shaped like a pyramid! It's prize is only 4 Bucks at amazon, and 10 at cubicle

Cubicle:
http://thecubicle.us/shengshou-pyraminx-p-155.html
Amazon:
http://www.amazon.com/Shengshou-Pyr...&qid=1433917182&sr=1-1&keywords=Pyraminx+cube
Another Shape Shifter is the X Cube, (or the cross puzzle). It's challenging too. I'm afraid it's 5$ Above your prize. It's 30, but i think it's worth it, however it's your choice

Here:
Amazon:
http://www.amazon.com/Moving-Parts-...33917314&sr=1-3&keywords=ShapeShifting+Puzzle
Cubicle:
http://thecubicle.us/calvins-3x3x5-cross-cube-p-1909.html
Hey, These were just some suggestions! I'm glad to help at any times

Tell me what you think