getting the elctric cigs is not inhaling smoke, part of the addiction is in the action. You get pleasure from feeding your addiction, the act of doing so gets associated with the act of feeding your addiction. Thus, the act of inhaling smoke is sometime enough in itself to feed the addiction to a certain point, even if no nicotine is present. Pleasure centers of the brain still become more active. Taking away the smoking aspect of the addiction will most likely reduce the activity of the pleasure center due to the act alone, thus breaking part of the habit. Making this a new habit it a bad idea, but a big first step is simply to break from the habit, to throw things off, to make yourself vulnerable.
This is why switching to a shitty brand helps. You don't WANT to smoke that brand or that electric cig. While patches and all that are good, it is more constructive in the long run to actively quit smoking. Doing very obviously things to change your daily routine will make the act of smoking ACTIVE rather than passive. You want to be DOING it, not having it done to you. You will stick with your actions more. It will be a stronger quit. Even if you chew the gum, I bet you will find that you are taking in more nicotine and chewing more gum than recommended (more nicotine than you would have simply by smoking). This is because you aren't participating in the act you have associated with your nicotine delivery system.
The best thing to do is slowly stop the act of smoking, then go to teh gum, then switch it up every once in a while. You don't want to get addicted to the gum or the patch. One thing you can do with the gum, if you become addicted, is to chew half a piece of the nicorette while chewing a full piece of other kinds of gum. The flavor of the nicotine gum will activate the pleasure centers in your brain associated with getting your fix from the nic gum, while you realy aren't feeding your actual nicotine addiction.