I believe you can do some PHP jiggery-pokery here, what you'll want to do is on the template page use PHP to detect which form was submitted (you could set a hidden POST value here, or check the posted collection parameter maybe). Then do unset($_POST['field_id']); for each of the fields on the other (not to display validation messages) form.
If there's no value in the $_POST it might not throw a validation message, but I'd have to double check this.
I'll try to spin a test up later this week for you, otherwise I'd definatly inspect the $_POST array on this template after submitting an invalid form