Testing Stochasty's method now... so far, I'd like to note that at least the entirety of step 4, the first screenshot of step 2, and channeling out all but the 1 cave-in trigger tile on S1 (in step 5) can and probably should be done before doing the "step one" chicken run, as that should train your miner from 5 to 7-8 already. You can also prep the gopher-holing of the wagon etc. as part of the training.
update:
Ok, so here's my go, a 1x1 pierce, with pictures. I won't go into all the details, just wanted to show a 1x1 shaft/fill in some details/show what I maybe did slightly differently. I'll use the same notation as Stochasty.
S1, all dug out before chicken running. The training areas were 2 11x11s and a 5x11 btw, that got my miner (strong, but average agility) to 10.
S2, again before the chicken run. I dug out that 1 tile off to the corner because Stochasty had a similar one, but didn't find any use/need for it.
A1, after successful chicken run and a couple of stairs/edge channels dug out. I did my first chicken run when my miner had 8 skill, didn't work out, fills up to 4/7 too soon. For some reason I picked the inner ring to do the first couple of attemps, but if you use the outer ring, and attempt it on every 2nd tile, you can actually do 12 attempts of the chicken run ((1 per corner and 2 per side between them), so you don't really need anywhere near 100% chances. I still would've had 6 more attempts even with the initial inner-ring ones losing me a couple. The NE corner was a failed run at 10 skill, but it's already been dug out in the picture.
A1 and A2, with the double rings of stairs and channels on the outside done. Unfortunately, my miner chose this point (mid-slate) to fall asleep in the SW corner of A1 stairs (was just blinked out in the screenshot), so any timing measures will probably be off. 1½ months should definitely be possible to pull the whole thing off, possibly even faster, especially with an agile miner (my only agile embark dwarf was also flimsy and weak, so this guy was the better choice IMO). This was just an aquifer pierce test fort for me, so the embark was in a badlands with saguaro/grass, and even a couple of pools (that maybe will evaporate in summer), and I brought food and booze besides the pick and wagon wood. I think the aquifer is salty, though, since the biome borders an ocean.
Ready for the drop. Channeled out the stairs on S2, which is the one thing in my order of doing this (I think) that could've been done earlier for miner training, but I kept them for faster access around the work area (no need to go to the stairs in the tunnel). Removing the inner ring of stairs on A1 actually isn't at all necessary, I think (Stochasty channeled them out, too, and then had to build a floor to get access to the plug). I just removed the up stairs, which has no effect I think, since up stairs don't support walls diagonally up from them anyway.
Aquifer levels after the cave-in. My dwarves can access the down stairs on S2, and from there the outer (now only) ring of up/down stairs on A1, the ring of down stairs act as floors, allowing access to the center. There was claystone (with tetrahedrite!) beneath the aquifer levels, and even with my messing about, and the miners drinking, eating and sleeping by now, the pierce was done on the 23rd of Slate.
So yea, it's possible to pierce a 2-level aquifer in 1½ months, with just 1 pick, NO LOGS NEEDED. Kudos to Stochasty for writing up the mini-chicken run+drainage method, I just found out where you were wrong about needing even that one log.
No logs needed means you could wall off the tunnel from the gopherhole, which can also be your dwarves' initial access underground, as soon as you cave-in the cart down and haul the logs, and be
completely safe, no surface access even from fliers. This should be doable within the first minute or so of embarking, right? And AFAIK this method should also work fine in freezing biomes, since water doesn't freeze underground, so you're safe from fliers there too. Now I'm getting the feeling that I/we broke the "challenge" of the single pick challenge, reducing it to a matter of luck, basically whether you get any hostiles pathing too close to your initial location before you first get your dwarves underground.
Well, there's still the matter of safely getting rid of the draft animals, and stabilizing the fort in terms of food/water.