Turns out that Evan Larsen has the best answer. Please upvote his answer (and/or select it as the correct answer) - it's brilliant.
Using Evan's trick, you can instantiate all tooltips with one line of code:
$('[data-toggle="tooltip"]').tooltip({'placement': 'top'});
You will see that all tooltips in your long paragraph have working tooltips with just that one line.
In the jsFiddle example (link above), I also added a situation where one tooltip (by the Sign-In button) is ON by default. Also, the tooltip code is ADDED to the button in jQuery, not in the HTML markup.
Popovers do work the same as the tooltips:
$('[data-toggle="popover"]').popover({trigger: 'hover','placement': 'top'});
And there you have it! Success at last.
One of the biggest problems in figuring this stuff out was making bootstrap work with jsFiddle... Here's what you must do:
NOW you are ready to go.