You're making lots of assumptions.
1) That client DNS systems will actually honor such a TTL. Many
don't (claim they're broken all you want, but these are the facts).
2) That client SOFTWARE will actually go back and ask again for the
IP number. Several won't (Netscrape being rumored to be one of
them). TTLs are irrelavent in that case.
Go ahead and try to tell your customer, who purchased web service from you,
that you have the right to disrupt their operations at any time and under
any pretense and see how many of them you have left.
Leave the site running on both IPs for (say) 4 weeks. Even broken DNS
doesn't last this long. And yes, anyone who doesn't quit their web browser
for four weeks will suffer, but these are mostly UNIX guys anyway who will
know why it's broken