Adaptation does take time but will improve the swim effect and skewing of lines. The first week is the worst, most people can generally adapt by the end of a month.
There are many manufacturers and many designs. A lens that is a short corridor lens will have more distortion than a standard lens; short corridor is used with frames with a relatively short vertical height. Free-form lenses grind correction on both the front and back surfaces which helps decrease some of the problems with older designs where all was on the back surface. There are specific designs for right and left lenses.
Best thing to do is speak with a very experienced optician who can help get you into the right size frame and lens design. Explain what you are experiencing with the current pair so they can help by adjusting the location of the optical center and the add zone.
More than you want to know about progressive lenses:
OptiCampus.com - Continuing Education Course
but see Design of periphery for discussion of skew distortion.