What to do with feelings during meditation?

A bloom in Olbrich Gardens

In "No Bad Parts," Richard Schwartz praises some aspects of meditation and mindfulness, but criticizes how Buddhist meditation teachers understand strong feelings.  For him, strong feelings are "trailheads."  Whatever you feel strongly -- whatever makes your blood pressure go up -- is a trailhead to some important "part" of you that needs attention.

But in Buddhist meditation (like in a sounds, thoughts, feelings meditation) the goal is to watch feelings in a detached way, like they are clouds in the sky, like they are cars on a train that "you do not need to get on."  The idea is that they are passing, they are not "you."  A common phrase is "don't feed your feelings with your thoughts."

That makes sense to me -- when I tend to ruminate, I can feel myself spiraling.  I know that I if I'm upset at night, I won't be able to sleep if I don't find a way to not feed the feelings.

But Schwartz's idea makes a lot of sense, too.  You might be good at allowing strong feelings to pass and become quietistic (that's always been one issue for me -- when you train yourself to be non-reactive, what makes you decide to do something, to take action?). Schwartz would agree; he'd say that meditation can destress you, but that it doesn't address/confront the "part" of you that's acting out with the strong feeling.

I don't have a solution to this... I just thought I'd record my current observation about the split.  It kind of feels like a "Structure of Scientific Revolution" issue:  are feelings a "background" thing or "the main event"?