I also use vim for a lot of word processing/prose, and I format as I go, rather than having a catch-all command that formats all your text at once. By manually formatting as I go, I implicitly solve the problem you describe. I'm not sure if this fits your workflow, but I'll describe it below:
I use this mapping:
" Easy line wrapping/formatting
imap gq <C-G>u<ESC>gw}
Which I invoke whenever I want to leave insert mode after typing out text that I wish to format.
This mapping performs the following actions:
<C-G>u
Manually create an undo-block, so we can unformat the text if we don't like it;
<ESC>
Leave insert mode;
gw}
Format to the end of the paragraph. You can change }
to whatever motion you prefer. (I format as I go along, so I only format from my current position to the end of the paragraph, which works well if I assume the previous text in the paragraph is formatted correctly.)
So as you're typing out
New Hampshire Spanks the Elites
Panic Sets In On Clinton Campaign
Some Sage Advice for Hillary Clinton
You simply don't use the mapping to leave insert mode. If you're typing out something that you DO want to format however; use the mapping to leave insert mode, and everything's done for you.
EG a long series of text input:
Streaming video is becoming a larger and more important proportion of internet traffic with each passing year. Video data is projected to take up 80\% of consumer internet traffic in 2019, with over 70\% of that being delivered via commercial Content Delivery Networks
gets formatted into the following when I leave insert mode:
Streaming video is becoming a larger and more important proportion of
internet traffic with each passing year. Video data is projected to take up
80\% of consumer internet traffic in 2019, with over 70\% of that being
delivered via commercial Content Delivery Networks
And if I want to make an edit to some point of the paragraph:
Streaming video is REALLY COOL AND I LIKE IT SO MUCH AND SO DOES EVERYONE ELSE AND THAT'S WHY IT'S becoming a larger and more important proportion of
internet traffic with each passing year. Video data is projected to take up
80\% of consumer internet traffic in 2019, with over 70\% of that being
delivered via commercial Content Delivery Networks
This gets nicely formatted into the following as well, when I leave insert mode:
Streaming video is REALLY COOL AND I LIKE IT SO MUCH AND SO DOES EVERYONE
ELSE AND THAT'S WHY IT'S becoming a larger and more important proportion of
internet traffic with each passing year. Video data is projected to take up
80\% of consumer internet traffic in 2019, with over 70\% of that being
delivered via commercial Content Delivery Networks