I think there are probably a handful of issues contributing to your bow's lack of accuracy.
First, as mentioned, it's may be the fletchings. I see from the pictures that your arrows have the 2" fletchings on them. A lot of people have found that they don't provide sufficient drag to stabilize the arrow with certain broadheads. However, the fletchings may very well be more than sufficient to stabilize your arrows, if the problem is fletch contact.
Second, you might have a problem with fletch contact. You mentioned that your fletch might be hitting the cables of your bow. Any contact with the arrow will affect your shot, even the movement of your bow WHILE you are releasing your shot. That's why a lot of archers are switching to drop away rests with complete arrow clearance. Also on that note, you mentioned that the arrow rest you used is the "little rubber arm." If that is hitting your fletching as the arrow passes, it too will throw your shot off. If you have fletchings aligned differently (with the nock), then every time the rest hits the fletch, it will throw the arrow in a different direction. This isn't as noticable with field points because the drag of the fletch will straighten the arrow out quickly, but with broadheads the extra surface area catches the air & planes violently. Actual feathers are less affected by fletch contact, but it does still affect them. That's why traditional archers who generally shoot their arrows "off the shelf" tend to use feathers, and make sure that their feathers & nock are lined up the same on every arrow.
It is possible that you have too much or too little arrow spine, but since your problem seems pretty severe, I doubt that that's the culprit.
So, my suggestions are, take it into a pro-shop, they will be able to trouble-shoot it no problem. After all, that's their job! While you're there here's a few things you should ask them to look for, and in this order;
FIRST! Make sure you don't have problems with fetching clearance. You might want to buy a drop-away rest ($100-ish) or just a cheap shoot-through with minimum contact.
Once you know your fletching isn't hitting anything, get them to re-fletch your arrows with 4" or 3.5" vanes, and ask them to put them on with a helical twist instead of straight. One thing though, if you are using a cheap shoot-through rest, you'll need to have the fletchings on straight, or you go right back to the fletching clearance problem. In my experience, cheap vanes that are glued on with a helical twist shoot no differently than the new vanes with fancy features that make them spin, maybe even better. The spin you get from the fletching helps stabilize the arrows, just like rifling & bullets.
Get the guys at the pro-shop to check your arrows against an arrow spine chart & make sure that they have appropriate spine for your bow.
If your field points are not the same weight as your broadheads, get some that ARE the same weight. Broadheads will never fly like field points, but at least if you're using the same size points you can adjust your sights properly.
Once you've made sure that these are all done, get the guys at the pro shop to paper tune your bow, and pay attention while they do it so that you can do it yourself. Doing your own paper tuning is as easy as nailing a few pieces of scrap wood together & putting newspaper over them, once you know how to adjust your bow & arrows.
By the way, you DO NOT need to have your broadhead blades aligned with your arrow's fletching. That is basically an urban myth, accuracy isn't improved or degraded by lining them up. What should help is getting your arrow to spin, hence helical fletching.
Hope this helps, cheers.
Tim
