This is funny because Shaw's own IP range's reputation is poor.
Can't you just change the IP address? I'm pretty sure the new Data Centre can do it and have it switch over without us noticing.
I've done it with my sites a few times.... It is seamless if done right. The data centre should be able to setup both sites running simultaneously on two IPs with just the database linked (unless it is on the same server... don't answer this question out loud...
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Do you have access to another mail server to send out the e-mails? That is another option.