I would put my money on your current single-ended setup being better than inserting an active Schiit component for no good reason. Honestly you’d have to put a gun to my head to get me to insert any Schiit into my analog chain.
If you’re concerned that the Simaudio’s balanced out has some magical sonic properties over SE - it might in fact only be using half its circuitry for SE outputs, in which case the balanced outs *might* sound better (maybe). In that case I’d go for a Jensen ISOMax line-level converter (XLR to RCA) before anything else. I’ve used one of these in the other direction - taking a SE phono stage into a balanced headphone amp - and it sounded great; there was distinct sonic advantage over full SE in that particular case, because that headphone amp only used half its circuitry in SE (note: an amp with differential input stage wouldn't have cared whether SE or balanced).
Somebody else can speak the the potential usefulness of simple XLR - RCA adapters (Cardas makes nice ones) in this application, but both the adapters and the Jensen box are handy to have in your audiophile toolkit :)