How to transfer a domain name with 99.9999% uptime?

Your registrar is, IMHO, the least of your concerns. Your actual DNS provider (the folks who host your nameserver) is probably worth a little consideration, but it's still down in the noise compared to the rest of what you need to do to really reach 99.9999% availability.

Six Nines availability (99.9999) means less than 1 hour minute (actually exactly 31.536 seconds) of downtime in a year. If you're really intending to reach that level of availability and not just blowing smoke you should be concentrating more on your (distributed, redundant) network & server infrastructure, and at that point you can really host your own DNS servers in your multiple (geographically and topologically distributed) datacenters :-)

Just my $3.50...

Is it your goal to reach 6 nines of uptime or is someone else mandating it to you? If it's your goal, then it's admirable but unrealistic, improbable, and next to impossible.

If it's being mandated to you then the entity that has made the mandate is woefully unaware of what it really means, what it would cost to achieve, and is likely just regurgitating some pablum they heard or read somewhere.

If you're worrying about your dns/registrar instead of your 4 redundant data centers, your 8 redundant ISPs (two different pipes at each datacenter), and your trans-continental clustering failover hardware/software solution, you're looking in the wrong place.

Six nines is basically impossible. You can be down for no more than 30 seconds each year. 30 seconds! If it takes you 10 minutes to failover after a catastrophe, you've blown your 6 nines average for TWENTY YEARS.

Chances are, you're not going to be spending enough to make 6 nines realistic. It costs more than it's worth.