As big of a fan of front brakes as I am I think you should re-evaluate what those websites are telling you about front brake use.

The front brake is the primary source of stopping power, yes, and is more effective than the rear brake.

The front brake can and should be used more than most inexperienced (and even some experienced) cyclists use it.

That said, thinking of the front brake as the primary brake can be dangerous. Using it by itself can cause you to flip over your handlebars. It takes a fair amount of experience on bikes in general and your specific bikes to figure out just how much front brake you can get away with in isolation (or any of a number of other scenarios) without causing a major crash.

Rear brake doesn't have that problem (you may skid and slide out, but it's less likely and not as catastrophic as if you go over the bars)

I rarely, if ever, use my front brake without the rear brake also engaged just as much if not more. Though it can be done, I don't recommend anyone use the front brake without using the rear at the same time.

Thus in situations like you describe I signal with my left hand and then begin to brake with my rear (right hand). You shouldn't brake before signaling if at all possible, especially if you are riding in a group with people close behind you. They need that reaction time. After holding the signal for a few seconds I scrub off the rest of the speed I need to by applying the front brake as well (rear brake is still applied).

In an emergency where I need to stop especially fast I don't signal. I will call out "STOPPING!" or similar (In really nasty cases the warning has been known to be one of a few choice 4 letter words ) and hit both brakes at the same time without removing my hands from the bars. I try to give as much time as I can for people behind me to react without hitting me whatever is in front of me (also helps prevent the "over the bars" problem).