Should I use an external Phono Preamp

That preamp has two Phono Inputs (either MM or MC) with very desirable extensive configurability. If it sounds great, done, find another way to scratch the upgrade itch.

"A total of 12 analog inputs¹ are located in the C12000 Preamplifier module: six balanced, four unbalanced, and two unbalanced phono inputs. The phono inputs are no longer set up as dedicated for Moving Coil or Moving Magnet cartridges; instead, both are configurable as either Moving Coil or Moving Magnet with adjustable Capacitance and Resistance Loading, along with adjustable Gain in 6dB steps from 40dB to 64dB. This provides maximum flexibility for you to configure the C12000 to best fit your turntable(s), cartridge(s), and vinyl record collection."

You have a removable headshell, any need for a Mono Cartridge? Or risk buying a used cartridge to get something unobtainable these days. I got lucky with 5 used cartridges, acquired 1 mono; 1 sapphire tube, and 3 beryllium tubes (no tube cantilevers in production these days). Also got lucky and found a very rare NOS Stylus (microwall beryllium tube, .0005" thick).

If you still want to try a different phono stage, I suggest a Tube unit, but keep in mind, anything Phono is 'preferred', not necessarily 'better'. I advise having a return option.

I used to have the same front end and cart with a different phono stage. 

you may want to consider a Sony HAT1 SUT with your Cadenza cart.and feed the SUT into your MM stage before trying something else. 

To outright beat the performance of the C12000 phono you are likely going to be looking at mid 5 figure phono stages such as a REF10 or TP 6.5 II or Boulder 2018.. 

I have a Cadenza Mono cartridge also