I will first attempt to define “soul” so we can calibrate expectations on SQ with each other. To me “soul” or the ability to reproduce the emotion of the performer(s) and the composition on recorded music has a number of factors I will attempt to describe.
1: Lack of Artifacts: Reproduction without artifacts, whether digital glare or vinyl grove noise, timing variations, etc. is critical. Having a source component that reduces these artifacts is critical to “soul”. When you audition equipment you are considering, listen to the timbre or acoustic instruments and to the background between notes. The former shound sound correct to your ears. The latter should sound as “black” as possible.
2: Image Density: Personally, this is an attribute I consider very critical. For music to have “soul” it is necessary for the images to have a dense, organic presence. Some source equipment will image well with good sound stage width and depth, but the image density will be light. When auditioning equipment use a well recorded vocal pop or jazz album and compare the image density. For example, a Stockfish recording of Sara K or Katja Werka, Dream with Dean, Dire Straits Fade to Black, or Billie Eilish Not My Responsibility.
3: Detail Retrieval: Reproduction of “soul” requires the source component to be able to reproduce detail to the level that it reproduces second harmonic decays of instruments and hall ambiance. This is critical for a source component to not sound “sterile”. On any of the recordings mentioned in #2, you should be able to discern the engineered decays around the vocals. For hall ambiance testing I use the Linn recording Applewood Road Loosing My Religion, a single miked live recording. Pick the component that lets you hear best the variations in the three individual vocalists inflections and vibratos, and how the sound progresses out into the open air venue. On classical music, I use the 2L recordings Magnificat and Reflections where hall back wall and ambience is distinct. Choose the source component that reproduces there effects best.
3: Micro and Macro Dynamics: Reproduction of “soul” requires the source component to reproduce micro and micro dynamic detail. I do not speak about “slam” which is not critical and often can rob life if it is unnaturally intense. I speak of the detailed dynamic inflections that are critical to reproduction of what others call PRaT. Any of the test recordings I mentioned can be used to determine differences in dynamic “soul”.
Regarding R2R ladder technology vs. “chip” technology, my experience indicates while there are some broad generalizations, it is not the conversation technology but rather the analog output technology that effects “soul”. Some of the best and most expensive DACs use “chip” technology. Some generalizations, IMHO, are ladder DACs (Holo May, DCS, Denafrips) more laid back in their presentation from a staging perspective. Timbre is accurate but laid back as well. Images seem to also be lighter. This is to the liking of many. Chip or proprietary conversion designs (Mola Mola, Bricasti, AR) in general are more upfront in presentation from a staging perspective. Timbre is accurate but with more immediacy. Imaging is more dense. Recognize these are broad generalizations in my system to my ears. I do not prefer ladder DACs. These generalizations were based on head to head auditions. At the time I owned a Wyred4Sound 10th Anniversary DAC based on Sabre chip which excelled at reproduction of analogue “soul” and my opinion was backed up by many pro reviewers. I purchased a Mola Mola Tambaqui just for the reason you are looking for. It was better to my ears in lack of artifacts , image density, and dynamics, as well as timbre, giving music life. It is not perfect. It does not have the widest or deepest stage and while ambience reproduction is excellent directly around performers, it does not extend into the spaces between as well as others I auditioned.
My recommendation is to look for used offerings from Brisasti and Audio Research in you budget. Above your budget look at a used Mola Mola or DCS Bartok. The Bartok Appex sounds more organic (soul) than its predecessor. Please audition because all of us have perceptions of what produces “soul”. Hope my long winded post at least stimulates a thought process that assist you in making a decision.