So I messed up and printed a circuit board with 16 TSSOP pad when I actually need a SOIC-16 pad!!! Is there a clever way of somehow adapting the TSSOP pad to a SOIC-16 chip?
The fastest way to deal with this is to "Dead Bug" your IC. Find a clear place on your board to glue the chip to it, leads up in the air (hence "dead bug"). Solder 32AWG wire wrap wire to the pins, and to the appropriate pads. It will take some practice and patience.
Obviously, if you're doing more than a few, redoing the board is the better approach.
Adafruit makes breakout boards for 16SOIC and 16TSSOP parts on a single board, with one side SOIC:
And the other side TSSOP:
So if you had enough room around your chip (a big if, understandably) you could use a heat gun/reflow oven and solder paste on the TSSOP side to attach it to the main board and then solder your chip to the SOIC side. The pins on both sides are connected electrically by those through-holes, which are normally used for a row of pin headers.
If that's not an option then I'm going to echo the sentiment of previous answers and say that, for more than a few boards, you should just correct the layout and get more made.
Unfortunately there's not really any kind of adapter or way to convert the two package sizes. Although the pin pitch is:
TSSOP pin pitch: .635mm SOIC pin pitch: 1.27mm
which would make it possible to bend the TSSOP pins onto the SOIC pad, I really wouldn't recommend doing that. Another solution could be to solder Kynar wire onto the Pins of the TSSOP and then in turn solder that onto the pads, but again it's not really recommended as it's a fiddly job and is not really practical for more than a few boards.
Your best bet unfortunately would be to correct the design of the boards and get some more printed.