...but I didn't want to add another pick list to the form. So I guess without adding another picklist there is no way around it?
But I don’t understand why the alert email you’re choosing to send for Form A would include the {{lead.tokens}} for fields that aren’t even on that form — unless you were deliberately trying to include their current value for reference.
By definition, a field not on the form can only be updated by another form or by another back-end process. So the {{lead.token}} wouldn’t be blank, it’ll hold... whatever the current value is. That would be the same for any field.
You could leverage the method described here to act only on the contents of the most recent form post (no more, no less):