I transferred my domain ( simplifybits.com) using Route 53 and it successfully transferred.
However my domain is not resolving anymore :(
This is what my setup looks looks like
There are two buckets in S3
simplifybits.com
www.simplifybits.com
Route 53 configuration
simplifybits.com - A
s3-website.us-east-2.amazonaws.com.
simplifybits.com - NS
ns-1069.awsdns-05.org.
ns-31.awsdns-03.com.
ns-1556.awsdns-02.co.uk.
ns-535.awsdns-02.net.
simplifybits.com - SOA
ns-1069.awsdns-05.org. awsdns-hostmaster.amazon.com. 1 7200 900 1209600 86400
www.simplifybits.com - A
d3v4utl52t4eyk.cloudfront.net.
I had this same problem. Right now your domains still have Google as the name servers:
Tech Email: tech@simplifybits.com.whoisprivacyservice.org
Name Server: ns-cloud-d1.googledomains.com
Name Server: ns-cloud-d2.googledomains.com
Name Server: ns-cloud-d3.googledomains.com
Name Server: ns-cloud-d4.googledomains.com
It isn't obvious but go to the "Hosted zones" tab and select your domain. Then, copy the "NS" records. Now go to the "Registered domains" and select your domain. If you look you will likely see to the right that the "Name servers" still have Google. Click on "Add or edit name servers" and enter your name servers from above. The popup will keep adding lines for you.
It took me a while to get this right as, like you, I thought I had to only have the NS records correct but that isn't enough.
As @steve-harris points out you will still have to have S3 enabled to serve static content but you'll want to get DNS going first.