In case anyone is interested, we were eventually able to solve this with the help of Eloqua Support and our IT department. It turns out that our IT group needed to make some changes to the way our sending domain was set up. Specifically, IT had to add the following string to the TXT record
v=spf1 include:_netblocks.eloqua.com -all
This authorized our sending domain to send from the Eloqua IP addresses. Once this was set up, our emails came through. So thank you to Eloqua Support for providing the answer!
Andy