Multiple Credit Card Charges

Obviously, when we tell them that the only way these duplicate charges can occur is by actions that they take during the transaction - they immediately become very defensive.. i.e. not taking any blame for the multiple charges...

Well, I'm not sure what to say, but you may need to take a strong stand with the client and try to bring them to a better position - i.e., not so dang defensive, and instead they need to be helpful.  Perhaps refer them here to talk to the forum.  It's not like this is unheard of, but OTOH there are known general causes and solutions.  If they want to be hard-headed about it, there isn't much to do if they don't want to listen.

We also use NOVA (now Elavon) having this issue as well.  I always think it is the user.  Double click, oh wait the billing address needs to be changed after clicking pay, etc.  What we do every day is:

 a) Confirm all payments for each invoice before it gets shipped.  We had once one marked in the BO as being paid, but it wasn't in NOVA.  It's a good accounting practice to check on payments anyway.  Doing this will also reveal double charges.

b)  On the end of the workday we log in one more time to check for double charges.  They settle our account around 6pm, but you can set it to whatever time you want with NOVA.

What this does for us and the customer is prevent overdraft charges to their account.   They may see douplicate authorizations to their account, but they will not settle, therefore no over draft fees.  Beyond that the customer needs to talk to their bank and have charges reversed.  We did have some unhappy customers over authorization charges, but we always ease them by telling them that they will be gone the next day.  Blame it on technology.  LOL

Now I think the customer has some rights if all the charges do get settled and they do occur over draft fees because you refunded the extra charges at a later time.  It's better to prevent them in the first place.

I don't use that disabling code, didn't know about it until I read this.  I didn't bother much either, since it is so infrequent.  I agree on preventing it all together, but I think their is always someone who manages it somehow. 
Another thing that may help you is in NOVA that you can sort the daily transactions by payment amount, that will help finding duplicates if you have lots of orders.  I also think there is some weakness on NOVA, since we do have infrequent order that show as being paid in PC and they are not in NOVA.  You better check that way around too, because you may be shipping orders without payment.  So good accounting practices are a must.  We print all orders twice, go into NOVA, stamp our copy as being paid, and release the order for shipping.  We do the same the Paypal.  At this point you will notice duplicates.  Perhaps you can also add the check duplicate routine to your end of day practice in the accounting department.  It should not take long at all.