I deal with sorting our other peoples' interpersonal issues at work sometimes. Here's what I would ask someone in your position to do:

1) Talk to the two women directly. Be polite and friendly. Do not put blame on them -- only describe how you feel and what effect the talking has on you. No confrontation! Conversation only. Try to have one (not more) other person with you to bolster your position and act as a witness. If you are afraid they may raise issues of gender harrassment, have the other person with you be a woman. Keep in mind that from the point of view of these women, they are not out of line. They have never been told so by their supervisor, who is the person who sets the tone of the workplace culture and ethic. Going over their heads without talking to them first ensures that the situation becomes confrontational.

2) If they respond with anger or other inappropriate emotion, end the conversation and go to your supervisor. Do not engage in an argument with them. If they agree to talk less but don't follow through, remind them once (in a light and friendly manner) and then go to your supervisor.

3) You have a supervisor who is incompetent to be holding the job he has. He is terrified of confrontation, and sometimes that is part of his job. It sounds like he has not responded to the idea that your work is suffering, nor to the idea that these women are being paid to sit around and chat. There are two choices when you have a supervisor like this. One is to provide him with more confrontation that he would experience by confronting the two women. This may cause him to mark you down as a nag and will certainly cause him to dislike you. You need to provide documentation of the problem along with the confrontation (the idea of making a tape was good). The other is to go over his head, after he has failed on at least two occasions to deal with the situation. This will also cause him to dislike you and may not be worth it. It may cause you to lose your job. It will also require careful documentation as proof of your charges.

4) It would be useful to have as much back-up from your co-workers as possible when confronting your supervisor or going over his head. It makes sure there is no way of anyone saying that you are just bitching about nothing. It is also completely inappropriate to conspire to foment a rebellion at work unless you have the support of all the rest of the staff and you are absolutely sure that the situation is making your workplace intolerable. I have fired people for forming cliques against another employee and harrassing them about their behavior at work when that behavior was inside the lines that the company had set as acceptable.

5) Keep a careful written record of everything you do!

6) When I say above that it may not be worth it, I mean that you should be sure of success before you start, or you should be ready to leave your job. If you are pretty sure you will not be successful, it would be easier to leave your job without all the hassle. Or learn to put up with the talking and laughing.

John