Stax have made exclusively electrostatic and not dynamic electro magnetic headphones since 1938. They are widely recognized as the ultimate in headphones, with a price to prove it.
Now electromagnetic phones have impedances that range for 8 ohm to 600 ohms. The lower the impedance the more current the headphone amp has to provide.
Now the Stax phones you are looking at have an impedance of 170 K ohms. That is 170,000 ohms. So those phones require a special high voltage, low current amp to drive them. In addition the amp has to provide the polarizing voltage for the electrostatic diaphragm, which I believe is of the order of 100 volts DC. There are headphone specialist sites that can advise you on options.
Stax do make at least a couple of amps to drive their phones.
This is one.
Your current headphone amp has a max output voltage of 8 volts and is designed for headphones from 8 ohm to 600 ohm impedance. It can not provide the polarizing voltage for Stax phones. So you current headphone amp will not drive Stax headphones. The Audio guy gave you the correct advice.
I would use a Stax amp if you are really going for the ultimate headphone experience.