Yes, once exclusive in DT you cannot submit them to other sites. The trick is during submission, you have to uncheck the box where it says the photos are exclusive.
Either you wait 30 days (from my experience you will have to send them more emails asking to "honour" the contract and the 30 days, or you can also disable those pictures on DT and upload them again as non-exclusive ones. Both workarounds are a pain in the a**, I would go with the second option.