Another (perhaps simpler for quick mental calculation) way of looking at the math is to take off from the fact that each 6dB increase corresponds to a doubling of the voltage (and volume). So a 6dB gain increase represents a 2X voltage increase, a 12dB gain increase = a 4X voltage increase, a 18dB gain increase = an 8X voltage increase and so on. Therefore the 15dB+ gain increase you are looking for corresponds to about a 6X voltage increase, giving .3mv X 6 = around 1.8mv or greater needed from a cartridge to drive your phonostage to a 80dB+ output (yielding basically the same answer as Herman's formula above).
It's a pretty safe bet to assume that any phonostage which doesn't feature built-in attenuation control is designed with the assumption that it will be partnered with an active preamp (has gain), and not fed directly into the amp or passively attenuated, meaning it's conceivable that doing so (even with a HO cart) may not necessarily result in improved sound.
It's a pretty safe bet to assume that any phonostage which doesn't feature built-in attenuation control is designed with the assumption that it will be partnered with an active preamp (has gain), and not fed directly into the amp or passively attenuated, meaning it's conceivable that doing so (even with a HO cart) may not necessarily result in improved sound.