...and one can plan ahead, and reduce TTL well before making changes, then restore the longer TTL after making the changes.
I'm pretty much in that situation, with some web servers that are being moved. I have control over the domain names, sub-domains and IP addresses, but not the TTL. The [nameserver] hosting company has a 24 hour TTL set for all domains and cannot (or will not) change it. Even if my server move is going to cause some disruption to the service to others, it would be nice if at least I could get my own servers flushed out and up-to-date.
My only workaround at the moment is to configure the domains on my own server, and set the various sub-domains (www, mail, shop, etc.)to 'external' and enter the IP address for each.
Alternatively, I could use a different nameserver hoster, at least in the short term, such as zoneedit with its extremely short TTL (half an hour, or something like that).