The curious thing is that no other businesses that we are e-mailing with has caused us any problems
Not really - the block only occurs between you and parent company, so the blockage must be in that chain. If it isn't your ISP then it must be nearer to the parent. So as long as you do not email anyone who shares the same ISP or upstream mail relay as the parent then you won't have problems - unless they start to subscribe to SORBS.
Static IP address for our e-mails
- this wouldn't help, as your email MX records and mail server will be addressed by name, not IP address. The blocking is done by name, not by IP address. So if you change IP address and keep the same domain name, you will not have changed anything!
You would need to change domain name AND IP address!
And unless you address the reasons WHY you are being blocked, the new name would probably also get blocked.
I assume that you have discussed this with the Parent?
Cheers
SD