I invested a lot of time listening to digital front ends recently and my recommendation would be slightly off the norm:
Keep the Lumin as a streamer (I like the Lumin x1, it’s a very decent, nice sounding product!). IRC, it sounds good & is user friendly.
Buy a re-clocker / regenerator. IMO Ideon Audio makes the best ones; a mid-level model ("Master Time") will set you back around 5k, the top model about double that. This simple device transformed my sound
Then, get a high performance DAC and you’re set. The same company has a mid-range DAC called ION that I heard in Munich; it sounded very good (by which I mean definitely hi-end, commensurate with the level of your CH pre). In a DAC only iteration the Ion probably costs less than 15k, well within your budget for both. In fact, at your budget lvel you could opt for the "Absolute Time" which has SPDIF as well as USB inputs & accommodate your old cdp as well (if you have one).
You plug the streamer output into the "Time" and from there onto the DAC.