Free solution that worked for me: Set up a free account on cloudflare.com, duplicate all dns records (thankfully I have a simple setup)... but next time I will keep a backup zone file!

FYI - Instead of an Alias record on DNSimple, CloudFlare will allow a CNAME record for the root domain using "CNAME flattening".

You can now set CloudFlare's DNS service to "bypass Cloudfare" on all records by clicking the icon so you don't get any of their magic (unless you want it).

Then add CloudFlare's 2 nameserves to your domain as your first 2 name servers. No need to remove dnsimple's name servers.

Now you have 2 DNS providers in case one fails, just make sure the records are the same across them both!