Interesting read. Thank you.
My first reaction was I don't think I've ever done that to a vocal but I then realized that I have....

I think in the times I've done big notches like in the article I was also compressing the vocal rather hard, bringing the vocal back together....
Like everything else in making music, you do what works ... at that moment in time ...
There are days that notching out something seems like the best and only way to do it. It requires a really good eq that can do really tight bandwidths though (usually plugins work best for me in this regard).
Here are the few ways I approach it...
If it's a stuck overtone (something always present at a constant volume), a notch works great. If it only happens once and a while then I'll either start automating the depth of the notch or switch to frequency dependent compression. Sometimes it's a combination of both automation and freq-compression. If you have an actual dynamic eq like the BSS or something, that may work even better. Lately I've been having fun with Sonnox SuprEsser. I'm finding that I have great control with the frequency that I want to control and the compression time constants can be very quick and inaudible.
It's always a balance to make sure that everything sounds right when the peaking frequency is present AND when it is gone. I guess, ultimately, I only want to alter a sound at the moment I have to and no more. Meaning we're back to ... you do what works ... at that moment in time ...
In terms of your vocal example, I'd probably start with separating the sections of the song a little. Most likely the 1k areas are in the chorus and the low freq problems are in the verses (I'm guessing). So now you have 2 vocal tracks, verse and chorus. Just play with it. If it's just one word here and one word there I'd most likely just automate an eq for that ONE word.
Michael