It took me a while, and it's a very dirty design, but I've got the
Handling done using a very complicated method.
Some of the problems can be solved by the same generic answer - a four-wheeled design with a some sophisticated suspension or a crawler/tank, usually - or using blindingly-obvious solutions (in Mind the Gap, just a very long solid vehicle. In mission to Mars, just a platform used by a vehicle). The later levels get tougher... I don't like the "lucky shot" strategies that so many use (though they obviously work) - I prefer to build more complicated machines that don't need to be launched and timed perfectly.
The hell?
I just managed - while trying to explore more time-efficient methods of doing "Up the Stairs" - to make a machine which tears itself apart. Literally - it rips itself in two and goes bouncing off in different directions.
Here's
mine, based on the idea of two "stages" launching the "bullet" far over the blocking balls. Simplest solution I had - if the vehicle can't pass the blocks, just launch it above them.
EDIT: This design appears to work for other situations: Namely
Big Ball.
EDIT 2: Also, an
Epic Fail.
EDIT 3: To all ye one-uppers, here's
Around the Bend in 1 piece, by myself.
And also,
On A Roll without a single ball.
EDIT 4: And actually, why not
On A Roll, no balls, three pieces? Took a fine bit of tweaking...
EDIT 5: Some tweaking, and there you have it:
On A Roll, no balls, two pieces!
And to counter the minimalism, here's some
overkill. Even though the launcher already completed the requirement, the bulldozer-tank-hammer bit continues to demolish the wall and everything around it. Harr!
EDIT 6: Here's what happens before
this design worked: It
completely twisted itself.
Famine will be happy.
EDIT 7: TB, I'm running your machine (unmodified) to see for myself when it messes up. 10 minutes past, it only moved them about a millimeter...
Also, my first shot at upstaging you with my own design
failed. Caused me to wonder what happened at first.
EDIT 8: TB, 15 minutes gone and the first brick is about 5mm into the target. My second shot at your record made a
nice visual display, but was too efficient: 2 minutes tops.
EDIT 9: I relaunched both designs at the same time, with a stopwatch. Lets see who wins... or at least complete the task. I'm not sure mine can.. It's leading yours by a bit (yours barely moved), but then again, it didn't activate the big trap yet. 13 minutes into the race, yours is "leading" (as in, mine moved the most) - apparently the huge mass I added just moved along.

Restarted with an improved design on my end. I'll have to crack it! Five minutes into the race, mine barely moved. I'm not sure if it'll even complete the distance, if it keeps on like that. 15 minutes in,
mine is leading by a very slight margin - yours pushed some of the upper rocks a little more. Nice and tight, a battle between two different approaches to blocking.

22 minutes in, yours is puttering along at a steady (and slow) pace, and I'm not sure again if mine will complete the distance...

30 minutes in, it appears both
can finish, but won't in the next couple of hours. Mine is furthest behind at the moment... but then again, mine's a huge fat tower, and yours is more sophisticated - though I could see some points to improve on it.
38 minutes in, both appear to be stuck. Yours had
something fall on it, while mine
just doesn't seem to make any progress.
Actually not - 40 minutes in, a small change in both can be noticed. Still works! Using a pixelmeter shows: Mine is 340px left of target (center of circle to closest target area), yours ~245px. The race is on!

45 minutes in, yours already pushed off two of the smaller squares long ago, mine are just nearing the edge. My counterweight is just starting to leave the construction zone...
55 minutes in: whoops,
your design backflipped. Mine's still going...
slowly as ever.
90 minutes in,
closing in on the finishline...
95 minutes in,
just two small blocks - and reaching the target area.
120 minutes in, I've missed the exact point, but it's
FAIL. Epic, grand, historic fail. It worked for two straight hours, and then started crawling backwards. After literally pushing off a mountain, it stopped just short of the last two rocks and started crawling backwards, pushed off the bits on the left, and fell down. IT FAILED!
