The custom STK units themselves will handle at least 80W per channel, maybe even 100W (designers' opinion) BUT the SX-680 itself does not have the capability to support that. The power supply is not designed to support much more than the original STK units, it does not have enough voltage or current capability, nor is the gain in the voltage amplification sections great enough, or have the headroom (voltage) to make a large enough signal to drive the power amp to that level. They will handle higher power than the originals for longer times, sound at least as good, if not better, and are repairable. In other words you can turn it up more with less risk of damage, but you are not going to get a difference like night and day. As an analogy, you can put a bigger engine in a car and get more performance, put if you put too big an engine in you will break the transmission, twist off the drive shaft, break axles, or even twist your frame.
They custom ones were designed to replace/upgrade the STK-0050 in an SX-780, which is rated for 45 WPC. The manufacturer of the STK-0050 rated it for 50 WPC use. If you read that whole thread you saw there were lots of different amps that have successfully used that design to replace similar original STKs including (I think) 80W modules.