I do not have experience with the SOtM gear, but I think that you will like the improvements that a better server will bring. Typically you will get a cleaner sound with a lower noise floor, primarily due to better clocking and reduced EMI in the server. This will not result in a more clinical sound, but you will hear more of the music.
If you upgrade and find the sound too detailed or clinical, then I would look elsewhere for the source, with your DAC being the likely suspect since you like your system already for vinyl.
I have had a number of digital 'aha' moments that caught me by surprise. (e.g. USB cables matter, somehow) I say go for it.