Bob,
Besides the obvious irritation for your operations at the airport, these new students are being given improper instruction. They will learn that blocking taxiways is an approved normal procedure. Then over time your issue with just one operator will become the norm. Everyone will be blocking taxiways and not just at your airport.
Years ago a nearby airport had an instructor who was not the best quality from the perspective of being a professional. His students were not taught the meaning of a traffic pattern. They would come and go from any direction which they chose. As a result it became impossible for me to control the traffic pattern at my airport. After several years of banging my head against the wall I finally gave up as I was becoming a basket case. As a result traffic patterns at all of the airports in this area are now nonexistent. The sad part of this is that the DPE was also rather lackadaisical, so as a result the students had no trouble passing their flight tests. They all passed. This examiner would even issue certificates based on phone calls.
Don't give up. The issue at your airport needs to be nipped in the bud NOW!