The Rega MM cartridges (Mike mentions getting a new Exact) have a very high output at 6.8 - 7.2mV so yes it sounds like something is wrong with the phono pre-amp or it's settings.
I am assuming Mike has already moved the output from the phono preamp between a couple of line level inputs on the amp to see if the problem moves with it (or not) and checked any settings etc.
My TT/phono preamp gives a 'slightly' lower volume than other sources but only needs a very slight tweak on the control. (5 or 10 percent maybe)
I can see the Moon LP3 has a lot of user adjustable settings going on...
£ End-user adjustable impedance loading (100 and 47k ohms)
£ End-user adjustable capacitance loading (0 and 100pF)
£ End-user adjustable gain for moving magnet (40dB) & moving coil cartridges (60dB)
Assuming you have set the correct impedance and capacitance for a MM, then it looks to me like you need to adjust the gain. (40db for MM)
Here is the manual if you dont have it already...
http://www.simaudio.com/pdf/MOON_LP3_Manual.pdf
Good luck checking all the internal jumper settings are correct! (Don't they have switches in Canada?)