Why not use a linestage after the phono stage and plug your headphones into the linestage, assuming it will add enough additional gain to drive them?
Unless it has a specifically designated headphone output, a line stage preamp will usually not be able to drive headphones properly. Quality dynamic headphones typically have impedances in the range of 32 to 100 ohms, which is much too low in relation to typical line level output impedances.
Also, dynamic headphone sensitivities tend to be very roughly in the area of 100db for 1 mw (milliwatt) in, the 1 mw representing 179 mv (millivolts) if the impedance is 32 ohms. 179/0.8 represents a gain of 47db. Since that is in the same general ballpark as the gain required to drive a typical line level preamp input using that cartridge, I suspect that the gain to the headphone output of the phono stage is the same as the gain to its line output (in this case 30db), the two outputs probably differing only in that the headphone output provides a buffer stage with low output impedance.
Bottom line: The phono stage is simply not suitable for a 0.8mv cartridge.
Regards,
-- Al