the beta trolls are the pre-scratch ones; they came first

Actually no. 

The Beta Trolls are the post-scratch trolls.

They are called the Beta Trolls because they interacted with the Beta Kids.

The Beta kids are called the beta kids because they played the Sburb Beta

The Alpha kids are called the alpha kids because they played the Sburb Alpha

There was no alpha or beta Sgrub, there was simply Sgrub.

And since the Pre-scratch trolls were dead during the Alpha Kids’ time and could not interact

There really aren’t any Alpha Trolls

Unless you count the ones in the Alpha timeline which would be Karkat, Terezi, Gamzee, Kanaya, Aradia, and Sollux, but that would make them both Alpha and Beta trolls

So in my opinion, I suggest everyone abandon the terms alpha and beta altogether unless talking about the Alpha timeline and simply use pre or post scratch to direct attention to whichever group they are speaking about.  It is simply the least confusing way.

~Mod T