I have done two conversions of my blogs to custom domain. The first one, Blogger Book went well with no hitch. The second one, this blog which is now www.bloggertipsandtricks.com met a hitch. The domain was purchased and registered direct via Blogger Settings > Publishing cum Google Apps. This time, the blog was in transition for 3 days. On the third day, there was a big problem. Neither blogger-tricks.blogspot.com nor www.bloggertipsandtricks was accessible. I quickly changed back from custom domain back to blogspot.
I wonder if the reason for the problem this time was because when converting to custom domain, I completed the captcha (word verification) many times. I did not see the message "changes saved" at the top of the page because each time I completed the captcha, the box for completing the captcha appeared again and I thought I made a mistake, so completed it again.
I did not try to meddle with CNAME and ANAME. What I did was repetitively switched back and forth from custom domain to blogspot to custom domain many times. After a few days, somehow the problem solved by itself and this blog is now published to the custom domain www.bloggertipsandtricks.com
I have read many reports of blogger having problems with custom domain. So my advice to you if you want to go this route not to purchase and register your domain via any third party. Do that direct in Blogger within the blog SETTINGS > PUBLISHING. Google Apps will do everything for you. The conversion should proceed seamlessly without you having to do anything. Everything is automatic though the blog will be in transition for about 3 days.
If you meet any problem, try switching back to blogspot and then to custom domain until the problem is solved just like what happened to me on this second coversion.