Well done! I wasn't even aware you guys were planning on migrating the site and I didn't notice the outage at all.
In the future, you can mitigate some of the DNS pain by contacting the DNS provider at least 72 hours in advance of a planned record change and having the Time-to-Live (TTL) on the host (A) record for
www.overwritten.net lowered to something short like one hour (or whatever the minimum that the provider allows is). Then, ideally, any outage that anyone experiences is no more than an hour (or whatever the TTL is set to). Afterwards, you can change the TTL back to eight hours or 24 hours or whatever it was before.
The TTL is related to how long a DNS client caches the record. A long TTL means that the client will cache possibly old information longer, but it means less hits on the DNS server because clients won't query for the records as often.