Which program do you guys prefer for adjusting your final speed? Timewarp is pretty slick in Premiere Pro; is the Timewarp effect in AE the same? Can you get a smoother transition from frame to frame using After Effects? Can anyone explain what the different Timewarp settings in AE are and what they do? Can anyone recommend a remedy for the headache this gives me? Why is the sky blue? Mommy, why do I look like the mailman?...

In the latest version of AE, the frame blender (I guess this is what you're talking about) has been added a new optical blend, inspired from Shake, Furnace Kronos, or Twixtor. Instead of simply blending frames together, an automatic warp does transition between 2 frames, meaning you can slow down as much as you want, as warp will simply takes more time to to the transition.

Be aware that oddities may (should I say will ?) appear with the warper mode...

When frame blending is ON with dotted line, it means you are using simple frames blends to transition between frames. The full line indicates the optical/warp mode.
Note that optical blending is far more render intensive.

In a global way, I think the less you do in NLE software, the better it is. No NLE will ever beat any image manipulation package, in terms of control, features, finesse, etc...

ps : for the mailman, I'm afraid you need to ask your mum directly