Congratulations on your ARC equipment. I have been a fan of ARC for forty years and only slowly over that time were able to buy, used at first and finally moving up over the last few years to all Reference level Audio Research gear. You can see my system under my ID.
While I agree that your gear requires the top notch interconnects, cables, and power cords to get the most out of them. I don’t think I would necessarily buy it all at once and the brand your dealer is recommending. You may want to take your time and find the brand that is perfect for your tastes. Transparent are a known synergistic brand with Audio Research and the one I use the most of.
$15K is perfectly reasonable given the equipment you are talking about. If you have good gear 10 - 20% the value of your system is a good rule of thumb. The most likely big gains are likely to be the speaker cables and power cord for your amp. I use Transparent Ultra speaker cables. ~$5K, but after a year of trying to figure out the correct power cord for my Audio Research Reference 160s I found The Audio Quest Hurricane (2 meters, I have a 1m and 2m on the Ref 160m monoblocks I am currently using the 2 m sounds better) . I also experimented with all my other components and found Transparent sounded best.
I have spent a lot of time with Cardas, WireWorld, DHLabs, Harmonics, Nirvana, and several other brands. With Audio Research gear you want really transparent (not warm or cool, low noise) wires to get the very best from them. Maybe Stage III interconnects are great… never heard of them. Dealers can’t carry a lot of brands, so they carry what they can… but always recommend that.
I could write a thesis on this subject and would be happy to have a more in depth discussion.