I'm editing a story right now, and they use this construction with no speaking verbs a lot:
Rachel was finishing washing the dinner plates, “I know this will be hard on them, but Shelby needs to go on home."
I know you could replace that comma with a period, but I wonder if it's common to use a comma or semicolon to avoid slowing the reader too much?
This next one makes more sense to me because laughing could conceivably be a speaking verb:
Maddie's laugh was laced with sarcasm, “Mark, looks like you’ve got a friend.”
That one could even be a colon...
Am I overthinking this? Should I just replace them all with periods?
Not just "subjectively extremely correct", the reader understanding your intention is the literal definition of communication.
The problem as a writer, though, is that you don't know if the "as long as" is going to hold. Punctuation as a set of rules that must be followed is certainly unhelpful nonsense, but punctuation as a tool to help point those who might be misdirected without it is worth some consideration.