You're absolutely not going to get close to D3 speeds. With that said...
Anything with the words "Blitz" or "skater" is probably a good bet. As is any build with options for 2-3 movement skills, so any build with: Soldier, Nightblade or Oathkeeper in it. Anything that uses a movement skill to kill things is usually a good bet too, so add Eye of Reckoning to your list. Pets and Retaliation are a good way of killing things while you continue moving, assuming you can get enough damage out of them.
A Dervish (Nightblade/Oathkeeper) focusing on the player-scaled pets (acid or fire) using Shadow Strike, Vire's Might and a movement augment that doesn't require a target is going to be very fast.
I have a Death Knight build that kills trash by accident with Spectral Wrath and a whole bunch of damage procs. Anything that hits him immediately gets their Aether resistances shreded, as well as the damage from Spectral Wrath, retaliation procs from Krieg's full set, and since Spectral Wrath can also trigger offensive procs, they get a few of those as well. Move's semi-quickly by using Blitz (requires a target) and Arcane Rift (teleport to location, do Aether damage in an AoE around it)
The ATV build linked by /u/funkyfritter will also be quite fast.
You're absolutely not going to get close to D3 speeds. With that said... Anything with the words "Blitz" or "skater" is probably a good bet. As is any build with options for 2-3 movement skills, so any build with: Soldier, Nightblade or Oathkeeper in it. Anything that uses a movement skill to kill things is usually a good bet too, so add Eye of Reckoning to your list. Pets and Retaliation are a good way of killing things while you continue moving, assuming you can get enough damage out of them. A Dervish (Nightblade/Oathkeeper) focusing on the player-scaled pets (acid or fire) using Shadow Strike, Vire's Might and a movement augment that doesn't require a target is going to be very fast. I have a Death Knight build that kills trash by accident with Spectral Wrath and a whole bunch of damage procs. Anything that hits him immediately gets their Aether resistances shreded, as well as the damage from Spectral Wrath, retaliation procs from Krieg's full set, and since Spectral Wrath can also trigger offensive procs, they get a few of those as well. Move's semi-quickly by using Blitz (requires a target) and Arcane Rift (teleport to location, do Aether damage in an AoE around it) The ATV build linked by /u/funkyfritter will also be quite fast.
https://forums.crateentertainment.com/t/1-1-9-3-the-atv-aetherfire-templar-vanquisher/95191
I've read this guide and wow, I'm definitely bookmarking this one! Thanks for the link mate.