I strongly agree that source material has a HUGE impact on how a system will sound, and the right "LP pressings" is the source material that offers the most potential for reaching the pinnacle of this hobby.
However, I'd say that using a record to make a system change is less about "fine tuning" and more about discovering that a great sounding copy of a great record and others like it (meaning other extremely high quality pressings of other titles) requires that we build a system that can bring the recordings on that record to life in the most convincing and satisfying way possible.
IOW, once you start playing truly great sounding records (I'm talking vetted, vintage records here, not the so called "audiophile" records that are released these days) you realize that you need to go back to square one and build a system that can actually play those records, because hardly any system can.
Therefore playing the right "LP pressings" is more about system design than it is "fine tuning". You want to start with those records, not finish with them!