Trying to configure DNS settings for herokuapp.com isn't going to work, given that it isn't, you know, actually your domain to configure.

What you should have is something like

  connoratherton.com     A     54.221.226.116
  www.connoratherton.com CNAME connor-personal.herokuapp.com

Alternately, if your domain registrar supports ANAME or ALIAS, you should have, respectively,

  connoratherton.com     ANAME connor-personal.herokuapp.com
  www.connoratherton.com CNAME connor-personal.herokuapp.com

or

  connoratherton.com     ALIAS connor-personal.herokuapp.com
  www.connoratherton.com CNAME connor-personal.herokuapp.com

I bet you could do this pretty effectively with GitHub pages instead of a full blown Heroku app.

Do you happen to have any extra invites for Google domains?

I do if still needed, drop me a line (email in profile)

Got one. Thank you to the folks on HN :)