I can't see why that would be a problem DNS wise. Although you'd be updating the associated A record rather than the MX record. An MX record is a FQDN rather than an IP address. The associated A record is what translates that FQDN to an IP address.
It would be advisable to set the Time To Live (TTL) on the A record as low as possible so changes propagate quickly to other DNS caches.
I'm not sure how you would workaround a block on port 25 though. Sure, you can run your SMTP server on an alternate port but there is no mechanism to inform remote MX's what that alternate port is - they will just expect to be able to connect to port 25 on your MX.
A quick google brought up http://domainmx.net
who offer a service to act as an MX relay - receiving on port 25 then relaying to your SMTP server on a non-standard port. I'm sure there are others offering the same.
Oh - and sounds like an hour faffing rather than a weekend.
edit - typo
edit again -
Just noticed that previous linkie is no longer accepting new clients. Maybe take a look at No-IP's Reflector service http://www.no-ip.com/services/managed_mail/inbound_p...
No-IP's been around for donkey's years and I've never heard bad things about them.
Edited by GeeTee (Thu 23-Jun-11 16:19:13)