To discover specific new biomes, you're better off finding them in the overworld, placing a portal there, and make roads/tunnels in the nether after that, to connect your different portals.
Even if it's very far in the overworld, the distance will always be divided by 8 in the nether.
Randomly creating new portals in the nether is a great way to load new chunks far away without having to travel too far, but to find specific biomes it's as random as it gets, especially now that the biomes are themed together.
For your grinder, supposing it's a good design, your only real option is to eliminate every other possible spawning block (or at least as much as humanly possible) by lighting up all caves and dark areas in a 128 block radius around your spawner.
I think he knows the locations of said biomes..he want to connect them or make travel faster to them from his base.
I don't know how to but there are mods like map or something..try map writer or something.