I made the jump years ago by going from an AVR to an amp driven the AVR, then to a combo dac/preamp which bypassed the avr entirely, then to a pre and dac separates. . My avr was not as good as yours. The biggest gain to be had is getting the avr out of the two channel system entirely (although I still have an AVR for HT use and use the external amps and speakers for HT, but the AVR/TV is off for two channel listening). The DAC and pre in the AVR are good, but not as good as well selected separates. Several small steps result in a big step. Honestly, you really need to try it and see how it sounds to your ears on your speakers.
BTW, I admire your room treatment and the effort you put in to improve your room before spending on electronics. I need to do a better job at that.