It sounds to me as if you don't understand the difference between a "charge" to your credit card versus an "authorization/credit" request (which usually appear on on-line displays as a "pending transaction").
I can't speak for why Delta and your CC were having problems communicating with each other. It happens.
Each time Delta tried again, it appeared as another credit request. These are NOT charges to your credit card, though most CC companies do put a "hold" on your account for the amount. In most cases, whenever a merchant seeks authorization for a particular amount, it means they are about to complete a transaction for approximately the same amount. After completing the transaction, the merchant must then submit the "record" of that transaction to receive their payment from the CC's bank. In the old day, this "record" was always the charge slip that you signed. In today's word, it's more likely electronic. For airlines it's electronic and the ticket number is the "proof" of the completed purchase transaction.
While errant/duplicate/erroneous credit requests do lower the amount of available spending (because of the "hold"), they are NOT billable transactions that you are liable to pay. After "x" days from the date of the credit request, if no record of the completed transaction is received, the CC will release the hold (and drop the "pending transaction" from on-line displays). Most folks have enough available credit that the holds don't affect them. Therefore these credit request (pending transactions) come and go without being noticed. If the holds are bringing you close to your limit, ten the CC wants somebody to review the acct anyhow and this is for your protection. If the CC feels a series of repeated credit requests are simply duplicates, then they will manually release the hold(s) as they did in your case. This scenario maybe new to you, but in the CC world it's just another day in the office.
If you still don't undestand the difference between a "credit request" and the completed transaction, then think of a restaurant bill.
At the end of dinner, your wait person brings you a bill for $100. You hand back your CC. They bring back an uncompleted "record of transaction" for $100. To have been able to print that record, they have already asked the CC for a $100 credit request and received an "approval code" (or a "credit denied" message). At this point, you have a "pending transaction" (and hold) for $100. You add a $20 tip and adjust the final amount to $120 then sign the record. Let's say today is your billing date and indeed, the CC is generation your new billing statement as you are filling out the record. The $100 "pending" transaction will NOT be billed to you. Not now, not ever, even though the $100 hold is on your CC acct. You hand the signed record back to the waiter. At some point after that, the merchant will submit to the CC wanting their $120 (minus whatever fee the CC charges them). If the merchant correctly sent back the authorization code of the credit request then the CC will remove the $100 hold at that time while at the same time creating a billable/chargeable transaction to your acct for $120. At the creation of the next statement is when you will be "charged" the $120.
So while your transaction with Delta this time was frustrating, it isn't nearly as bad as you're making it out to be. I highly doubt that Delta "charged" $6000 to your CC. They repeatedly asked for approval for $1500 of credit. As you stated, your call to the CC resulted in the 1st round of duplicate requests being manually removed. Your 2nd attempt in buying the Delta ticket created another round of duplicated credit requests, but Delta only provided proof of a completed transaction (ticket number) on one of them. Therefore, Delta only "charged" your CC for $1500 once.
My wild guess is that Delta was having temp issues on a server somewhere. They were successfully send out the credit requests, but were not getting the "approved" reply back from the CC. After a few seconds, the request "timed out" on the DLL system and replied back to your DL Agent with "approval code not received". Your Agent simply interpreted this to mean "credit denied" and a common reason for such denial is most likely an incorrect security code, so that's what the Agent told you.