Constructive & Helpful!
Basically, I'm wondering what the highest damage but consistent solo class is.
The obvious answer here, is Void Highlord, although that doesn't seem to be available to you at the moment. But aside from that, Lightcaster, Legion Doomknight (I soloed Aranx pre lvl 40 with LDK once), Glacial Berserker would be some good choices to go with, preferably Lightcaster out of the 3 when it comes to soloing Aranx. If you cannot solo him consistently with Lightcaster, I don't know what to tell you, Lightcaster is just "spam to win" and lag should be one of the last things that could get you killed while using it and Aranx isn't even one of laggy bosses to where it could hinder performance that drastically.
Shaman and Evo Shaman (mostly Shaman) also works pretty good at higher levels against Aranx, but does require a lot of proper mana management to get any good kill time out of it. I did it at lvl 57 or so with Shaman, but I came close to dying a couple times because of a couple crits in a row.
If you are going for Burning Blade of Abezeth, I would recommend getting to level 80 first, as you can't really use it before that level anyways. You technically can, but without being able to put an enhancement on it, it may not be worth it over just Burning Blade or the like WITH and enhancement on it, plus being that high levels will give you a better kill speed and lowering the chances of dying significantly. If you are just going for something else, simply stick to Lightcaster and spam your way of victory, it's one of the safest and speediest classes to do it with.