I downloaded the startup installer and had it download onto my second HDD which has way over the required space (have 350GB left), but the download gets really far then starts back from the beginning, really annoying, do not want to miss the beta!

Open a support ticket or ask on the right forums. We cannot help you here.

There is an official forum for ESO beta testers, access information should be at the bottom of the invite with your beta key. There are several other official support channels you can use listed there, as well as in the http://www.gamesas.com/topic/1483416-dedicated-eso-beta-discussion-thread/ thread here on Bethesda's forums.