An Etiquette Question

As I mentioned in a previous post, most of our Bat Mitzvah invitations have gone in the mail. Traditionally, one invites the congregational rabbis to the reception, understanding that they typically do not attend. But it is “what you do”. So, we have three envelopes waiting to be stuffed and stamped for the congregational clergy (two rabbis, one cantor). Here’s where I have a quandry. We know that neither of the two congregational rabbis nor the congregational cantor are available that day (for if they were, they would be doing the service). I feel weird sending them invitations knowing in advance they won’t be there. It seems like a slap in the face. So, the question is… should we send them invitations?