SN3 is IMHO a better amp than SN2 - it’s not just the MM phono stage - but not that much better. For your LP12 and phono stage, I’d think about a SN2 on eBay as a trial if you want to try further steps. If you buy it and don’t hear a material SQ benefit on LP and CD, you can sell it for (probably) little or no loss on eBay again, so the experiment may be involve more bother than net cost.
If you don’t stream as a priority, Bluesound may give you all you need. If you want a better DAC, the Naim nDAC is a second-hand bargain IMHO - its DAC is around NDX2 level in performance, and some here regard ND5XS2 (as streamer only) plus nDAC as at least as good as an NDX2. There are also lots of good non-Naim DACs of course - Chord is one Naim that springs to mind.