no one has created a nice high end stereo tube fit that is convenient and is a true ht bypass.I believe Rogue, VAC, and Backert make tube pres that may work in bypass mode without tubes glowing so might be worth checking out.
Anyway, in my system I get the biggest impact from interconnects closer to the source. I’d start with an Optical Rendu from router to streamer, then I’d replace the Monster with an Acoustic Zen Silver Reference interconnect (balanced if possible) as it’ll preserve all the detail/dimensionality of your DAC without adding etch or bleaching tonality. I think those two changes will make very meaningful improvements to start. Hope this helps, and best of luck in your search.