Jay,
Everything is important in the TT/arm/cartridge chain. But the details matter. I have had several turntables that were very different in tonal balance and other qualities, and it seemed that no cartridge would sound like what I wanted on a bad TT like the SOTA Sapphire. On the other hand, my Linn Valhalla and Goldmund Studio were much closer and both excellent, so the cartridge was more important in the overall sound quality.
Re: tonearms, on my Goldmund, I much preferred the more neutral sound of the Alphason arm over the Goldmund T3B straight line tracking arm. On my Linn Valhalla TT, I did more trials with different cartridges and different arms. I found that cartridge differences far exceeded arm differences, mainly due to the different tonal and spatial differences. Cartridge differences were quantitatively similar to speaker differences. It was like the big difference between a clarinet and oboe vs the more subtle difference between 2 clarinets.
Despite the generic pronouncements in manufacturer promotions, there is very little written on actual specifics. A good analysis would go like this. Take the entry level Linn Majik, middle level Akurate, top level Klimax TT's. Outwardly, they have similar design, look the same, but vary in materials mainly, but also in power supply quality. Add the Majik, Akurate, Klimax arms, then the Majik, Akurate, Klimax cartridges. There are 27 possible combinations of all these. The Majik cartridge is a moving magnet type, whereas the Akurate and Klimax cartridges are moving coils. All of the moving magnet types were vastly inferior in resolution/clarity to all moving coils I owned. The Majik TT is probably still an excellent TT, better than my much older Valhalla TT which was still fine. I challenge anyone to step up and say that he has heard all 27 combinations (in their own system and not at a biased Linn dealer) and claim that the still excellent Majik TT plus the top moving coil Klimax cartridge sounds worse than the Klimax TT with a grossly inferior moving magnet cartridge. I don't accept anyone parroting official Linn dogma about their hierarchy. Do the listening yourself, and report honestly. Don't merely say that one is better than another. A romantic Koetsu cartridge will certainly perform its "best" on the Klimax or other top TT, but what does "best" mean? More romantic, or more precise and less romantic?
All that said, I believe you are on the right track with the Kronos TT. From the review of the Kronos Pro in Mono and Stereo, the Kronos makes cartridge differences more dramatic than any other TT the reviewer owned, even the far more expensive Tech Das and Clearaudio Statement TT's. I recommend you spend good money on the top Lyra Atlas cartridge and settle in for now. Along with your top Boulder phono preamp, you will probably prove the superiority of that top analog system to your MSB and server digital system in nearly every way. Later, you can try other top cartridges like the Ortofon MC Anna Diamond, whose differences vs Lyra will be maximally revealed. And try the much cheaper Rega Apheta 3, with Oz's approval for cartridge/arm compatibility. The much more expensive Rega Aphelion cartridge is of similar design to the Apheta 3, and may be better or worse.
I love the Kronos design of the 2 platters rotating in opposite directions to cancel out vibrations. The Mono and Stereo reviewer particularly noted the strength of the Kronos in bass, so this TT may suit you best. But think about the lightweight Rega system, which Fremer thought noteworthy for midrange/HF clarity. Poorly understood is the effect of high mass/low mass and different materials in favoring different frequencies. Perhaps Rega is more revealing in higher freq, while Kronos is best for bass and still great full range.
So there is no easy, glib answer to the question of which component is most important. Nobody has done all the listening I suggested, and even if they did, they have not reported their findings.