OP, Sounds like spending $2 -3K is likely to benefit you. I recommend you rent, or borrow and verify they are worth it to you. If not, don’t waste the money until your system gets good enough for you to hear the benefit. Interconnect and cables should always supply an improvement of greater value than if you used that money to upgrade a component.
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After testing and buying interconnects and cables for my systems for over four decades I think there are some generalities that makes sense. In rare instances interconnects and cables can have a “component level” effect on performance ( I have experienced it twice). But typically in systems over $20K or so they should represent 10 - 20% the cost of components to get the highest cost effectiveness (this is not guaranteed, you have to do the work) . My components on average cost about $20K per box, and my interconnects are around $3,500 each. Seldom will the benefit be enough to justify $3.5K on a $5K component... the money would be better spent on upgrading the component. Having said that I did buy three sets of interconnects costing $2K each about 25 years ago for my $3.5K components and it was absolutely worth it (Nirvana SX-1 interconnect... yeah, they were that good).
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Low end systems don’t benefit much from interconnects because they are not that sensitive... so, work on upgrading components.
When you start spending over $1K per pair you should listen and verify before purchase. This is me, life is too short... on my office system... I just didn’t wan’t to waste the time... components only cost a couple grand each... I just read reviews and bought them.
Using interconnects and cables for tone adjustment can be a tool for moderate priced system... say < $40K... plus or minus $30K. As you get higher, your components have less eccentricities to be adjusted. For example, early in my audio life my components were too trebly and slightly harsh, exacerbated by my ribbon speakers. So, I artificially warmed them up... I used Cardas Gold Cross. .
As my systems got better, I needed interconnects and cables that were just more transparent... that did not have a sound of there own. At these levels very small changes in interconnects can have substantial effects on your system because it is so sensitive. But the same rule applies... I don’t think putting $15K interconnect on a $20K component... get a $40K component... then when you recover the expense (and upgrading all your other components) upgrade to $10K interconnects (obviously have your vendor lend you a pair to verify your are going to get the improvement appropriate .