I feel my lips a little more open and my cheeks a bit more puffed out with "bad".

Try this website: http://www.uiowa.edu/~acadtech/phonetics/english/english.html Look for "vowels, monophthong, front." The sounds you want are in the second column, second and third rows. I can hardly see the difference on that website and I can't even say what I feel when I say them. They sound quite different to a native English speaker who's used to hearing them. However, your speech will be easily understood if you use the wrong one.