Would it be worth it to send an update letter now and just include new honors, or should I wait and include new grades, even if they might not be all that great?
The beauty of an update letter is that they are not required and you need not include anything that doesn't reflect positively on you. Mention any class where you performed well, especially if it is relevant to med school. Do not include any class with a mediocre grade.
That said, if any of some grades will be worth mentioning, then I'd wait a few weeks until they're available to make the update letter meatier.