Workaround for servers that have blocked all Constant Contact emails?

Has anyone out there encountered a way around servers which have blocked all emails from the Constant Contact service in general?

We have self-authenticated our CC account and everything however we have about 100 users who have emails at a specific domain (one company) who has been so bombarded with CC emails in general that they have outright instructed their IT people to block every single email that comes via the CC service.

I have been in touch with the IT dept and regional managers, and they say they have no problem with OUR emails, however due to the constant SPAM-ming from other users, their CEO asked them to block all CC emails. They have told me that if I can provide them with a static sender's IP, they can create an exception to allow our messages however this is not a service that CC provides.

If anyone has encountered this and has any suggestions, please let me know.  Otherwise it may cause us to switch to another provider who does offer this service. 

Thanks in advance.