I keep saying silkscreen instead of solder mask, I even messed up the title... I know the difference, my brain is just glitching.
Here's an example of one of the boards that just shorts out some of the leads when they're tinned. My camera doesn't do macros well so I had to flood the board with a bright LED. It doesn't actually look like a disaster site, it's just a very bright reflection from flux splatter. The board is in the opposite direction this time, you can see the pin-1 square is on the bottom-left rather than the top-right.
From this distance (I can't get any closer) there's no visible bridging. Yet, pin 13 and ground have relatively little resistance between them (~20k), and pin 9 is practically shorted to ground (~500ohm).
I've been using the tin-and-reflow method. I tin the pads on the PCB, apply flux, place the QFN on the board, and then reflow with a hot air gun (with as low of a temperature as I can get away with, usually around 260c). The hole in the middle is to allow excess solder on the thermal pad an escape path in case I used too much. In this particular picture I didn't bother wicking it off, so there's a lot of it on the thermal pad, but I usually keep it to a minimum so there's only slight curvature on the solder "mound" in the center.
I was hoping to avoid using stencils because at this size my hand isn't stable enough to accurately place the package in one go, it's always off by a bit so the solder paste gets smudged around.