I'm not sure how in the world it's possible to complete the starter two Time Trial courses under 1:20 something. I always NEED 1:45 at the bare minimum to get through with my Lv60 soldier class w/ custom guns/armor. Is there a trick that I'm not figuring out?
 
Also I assume you unlock the last four courses by scoring in the top in the first 8?

set the game to normal?? i found the first 2 frustrating on insane and dropped it down to normal and it seemed easier
 
and yes you get the last 4 courses when you come top on the first 8 and when you come top in all 12 you getta special scenario

I didn't think to check my difficulty, does it alter the time needed to complete?

nah time stays the same

Okay because that's what I meant. I cannot finish in enough time, and I don't know what I'm doing wrong.

I'm playing on veteran and got 1:20:67 @ Warehouse and 1:18:86 pm Tropical. 
 
Warehouse took about 5 tries to do, but the keys i've noticed are 

• Your team mates CANNOT handle enemies on their own.  Don't run to the next area assuming your guys will land the final blow on a guy with only like 5% health left.  They will not.  You have to finish off everyone.
• Run as much as possible while avoiding fatigue as much as possible.
• Memorize where people come from because that won't change from run to run.
• Alot of it is luck.  Sometimes enemies live outside of cover and on another run they'll stay hidden in the cut and you have to waste time going through crates and barriers to get a shot on them.

That helps, I'll remember those points. It's just mind-numbingly frustrating.

I got it after lowering the difficulty and changing ammo types to be the most highly appropriate for the type of enemy that was spawning (either organic or synthetic but it's never both). Seems like it's just how much HP the enemies have that's really the deciding factor. Overall I'm pretty disappointed with this DLC, they spent like no time on it.

^
I wouldn't say that.  They made alot of new areas and the combat level design is way better than any combat scenarios you encounter in the actual game.

That's like saying, "I made creatures in Spore so I know how much time it takes Pixar to do character animation/design."
 
On a sidenote, nothing in these missions is hard enough to where you need to dial it all the way down to casual.  If you have to do that i'd say there's something about the combat system of ME that you don't understand.

Switching the difficulty to easy makes the combat scenarios incredibly easy.

I only went down as far as normal, but that's good to know now that I've wasted the time dealing with it =/

High explosive ammo knocks the enemy around without effort.
 
You team mates are not fast movers here, so you should direct them manually to enemy areas. Send them to each spawn location ahead of you and then do the cleanup while they act as a distraction.