First sentence:

> In my Ottawa life, every Tuesday evening, I take two gym classes back to back—boxing and the pompously named “body sculpt,” which makes me discover muscles I didn’t know I had.

The em-dash matches how you'd speak out loud.

You'd say "I take two classes every Tuesday back to back, boxing and 'body sculpt'. Weird name." (Parts of that sentence did flow oddly, but not because of the em-dash).

Grammarians say you can't make those separate sentences without adding some extra words, and because of blah-de-blah-blah-blah, someone might say you can't join them with a comma. So we have an em-dash.

Rewriting the sentence would make it flow less naturally, not more.