I haven't used those accelerometers, but from a quick look at at the specs and code...
It will take 20ms worst case to get a reading. If you need two axis on 7 cups that will be 14 readings, or 280 milliseconds. You could sample the who setup about 4 times a second. With really clever coding you could double that rate by watching several of them at once.
There are 14 inputs, but if you used them all you would have no outputs to do anything, you would have consumed your serial port. Fortunately there are devices called multiplexors which allow you to select one of many inputs. You could use a 16 channel multiplexor (MUX), that would take 4 outputs to tell it which channel you wanted then only 1 for an input leaving you plenty of pins for other functions.
There are also analog multiplexors if you went with analog sensors. You could probably get a higher sample rate this way if that was an issue.
And ah, the best.... Will people rip it apart? Absolutely! If it is possible they will rip it apart. Theymay not mean to, but it will happen. I might experiment with using a low stretch, braided sheath rope of the sort used by small sailboat sailors. This has a braided cover in a pretty color with a core of straight, very strong fibers. You can easily get hundreds of pounds of breaking strength in a few millimeters of rope diameter, but the best part is when you 'scrunch' the sheath a bit it gets bigger and you can snake a couple twisted pairs through the inside where they are protected. If you are very clever with your knot work you could encase the sensor in the rope as it is tied around the handle of the bowl... assuming they have handles... otherwise you will have to glue it on somewhere and hope for the best.