my speakers are very inefficient Vandersteen Model 2C’s from the late 80s.
As far as i know Vandersteen Model 2C speakers sensitivity is just 88dB, this is the reason why you need gain and powerful amp.
The reason why i love High Efficient speakers (97-101db) as the opposite to the average 86-88db, is the low power amp that can drive them easily, my preamp is passive/active. But i never use active mode.
If you want to solve the problem forever you may need to look for some high efficient speakers like Zu Audio or Tannoy ? It can be a revolution in your setup (if you haven’t tried some of them yet).
As for the cartrige with higher output you can try some with 5mV or even 9mV. Maybe you can borrow a $60 Shure M-44-7 (9mV output) to check your system with it.