Sounds like a rewarding process for the OP. Pardon the late response, but the low-hanging fruit for your next upgrade is to ditch the Bluetooth and never look back (unless you have one with the latest greatest BT tech, like the iFi Zen Blue) -- get yourself a dedicated streamer/DAC or a wifi receiver/DAC, of which there are plenty of affordable options, the Audioengine B-Fi being among the best.
Or since you have an iPhone, get the most bang for your buck by finding a used Apple TV (up to 3rd generation has optical output) or a last-generation Apple Airport Express (MC414LL/A), which has a built-in DAC and 3.5mm analog output AND optical output through the same 3.5mm port (https://www.kenrockwell.com/apple/airport-express-audio-quality-2014.htm).
Or since you have an iPhone, get the most bang for your buck by finding a used Apple TV (up to 3rd generation has optical output) or a last-generation Apple Airport Express (MC414LL/A), which has a built-in DAC and 3.5mm analog output AND optical output through the same 3.5mm port (https://www.kenrockwell.com/apple/airport-express-audio-quality-2014.htm).