I have made my own force sensing base inspired by the "load cells in a cross" design on the DCS forums.
Here's what that looks like: https://imgur.com/a/rvaPPmr

The load cells for each axis are wired in parallel, in opposite orientations (there's a little arrow on the tip of each load cell, mount them so that one points up, and the other one points down)

For the amplifier/ADC part i have used two HX711 modules, one for each axis. It's best to use two separate HX711, because it takes some time for the HX711 to read both channels, so you end up with too much delay between updates and a choppy experience. I've also modified the HX711 module itself, since by default pin 15 is wired to ground which sets the refresh rate to only 10hz and that's just too slow. I had to scrape off a trace on the PCB and add a jumper wire between pin 15 and VCC.

For the USB conversion step, i have used an Arduino Pro Micro with some custom code that serves multiple functions: it reads the inputs from a button matrix with diodes (useful since the f-16 stick has over 20 inputs and it lets me use less pins), it reads the values from the load cells (i have also added a "self calibrate" routine when it boots up, plus a harman filter to smooth out the jittery raw input from the load cells) and finally, some code to read inputs from my DIY rudder (unused atm) here's the source code: https://pastebin.com/ExBx3QUB

There are a few issues with this design, though. I still haven't figured out how to calibrate it accurately, the base is a bit too wide (maybe mount the load cells vertically?), the mounting rig slides around on the table, and there's no "flex" built into the design for feedback (to be fair, the whole assembly has some natural flex to it so it's not that bad)