You have very few options, generally
(a) convert people to evil religions so fewer units go to Basium when they die.
(b) kill Basium before the other good opponents.
(c) have a very big army.
There is more bad news. Basium won't submit while he is allied to another nation so you either have to kill him or kill his ally before either will submit. The 'good' news is that Basium frequently seems bugged and doesn't move his army outside his borders.
To be honest I don't particularly like Basium always appearing in the game and leaving you with very poor options dealing with him. Sometimes building the gate yourself is another bad option, since Basium does stuff like declare war and give your tech away to vassals. It's worse still when no civs are going to develop the Ashen Veil all game and yet Basium still comes in and blocks most quick routes to ending the game.
Hyborem, on the other hand, always seems to add spice to the game and pushes it towards a climax. It's the shame that the computer AI generally can't get him going. He's great fun to play though.