I would have thought you could get them much cheaper than that - I know there are RPM counters (tachometers) that are less expensive, but which probably don't have a trigger-on-count functionality.
Why not a basic TTL circuit or a micro? A dollar or two in parts and you should be able to fully configure it, a 12 bit counter, a comparator on the input set to your signal level, and some and/not gates to select where to stop if you want it hardwired. Also any old micro can do this in half a dozen lines of code, you just need a relay driver and whatever signal conditioning to get your input signal readable by a micro.