Probably: the least expensive experiment, in order to narrow down your issue, would be to purchase/mount the cheapest MM cart available and see if it results in a satisfying SPL.
ie:
https://www.turntablelab.com/collections/best-turntable-cartridges-by-price-ttl-levels
Alternately: an SUT (easier to install/more expensive, probably), but: may increase noise/hum.
Personally: I'd be looking for a phono stage, capable of outputting between 1 and 2V, with greater gain than 60dB in the MC stage.