Three points in this:
First, the BL17s, nice that they are are not good enough for the Altair, so I think your budget is more appropriate at the BL17 level
Second, I found the RCA to RJ45 did not trigger the BL17 on/off. The RCA to RCA works just fine.
Third, your streamer will need to have either electronic attenuation adjustment (-3, -6 and -12dB with -6 and -12dB being useful) or an external attenuator (variable or fixed) which when I attempted this…it sounded very bad.
A BSCore May be a good match and fully integrate into a B&O system and match the qualities of the BL17s. Personally, I did not like the core playing into the 90s so never tested it on the 17s as I have already migrated to an Auralic streaming system across everything in my home.