Welcome to Fastmail and the forum.
I don't think that changing your login address to use your private domain will necessarily do anything to improve your security, but would be interested to hear from anyone who disagrees.
I have a lot of different addresses that I use (private domains, employer, university, etc and also FM aliases -- probably similarly to most of us here), but I don't use my login username for actual email communications, so I've chosen as my login name (@fastmail.com) a sorta randomish string of letters that's easy to type. I
have thought that not having my real name (or anything else that can be traced to me in the real world) as part of my login credentials helps to improve the security of my email (makes it hard for someone to get in by guessing at creds).
As for spinning off individual addresses for each of the web properties you deal with, that's an excellent idea, one of the things I love best about FM and one of the reasons I will likely stay with them forever. I haven't found any other ESP that does this (at least, in-house). I make my individual addresses a little more (pseudo)secure by rot13'ing the left-side strings: thus "walmart" becomes "jnyzneg". It's more convenient if you can memorize the rot13 translation table
The weakness of this scheme, for me, is that I'm using an FM domain alias for all of them rather than a private domain, so that if I wanted to leave FM for another provider, I'm much less mobile. But it's not something that keeps me up at night.
https://en.wikipedia.org/wiki/ROT13